biografia de lions

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doi: 10.1098/rsbm.2002.0015, 275-287482002Biogr. Mems Fell. R. Soc.

Philippe G. Ciarlet 17 May 2001Jacques-Louis Lions. 2 May 1928

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JACQUES-LOUIS LIONS

2 May 1928 17 May 2001

Biogr. Mems Fell. R. Soc. Lond. 48, 275287 (2002)

Lions for press 9/12/02 10:39 am Page 275

http://rsbm.royalsocietypublishing.org/http://rsbm.royalsocietypublishing.org/http://rsbm.royalsocietypublishing.org/


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JACQUES-LOUIS LIONS

2 May 1928 17 May 2001

Elected For.Mem.R.S. 1996

BY PHILIPPE G. CIARLET

Laboratoire dAnalyse Numrique*, Universit Pierre et Marie Curie,

4 place Jussieu, 75005 Paris, France

Jacques-Louis Lions was born in the heart of Provence in the charming city of Grasse, muchrenowned for its perfume industry and its historical centre.

In spite of his young age, he had the courage and determination to join the French

Rsistance at the end of 1943, as a soldier in the FFI (French Forces of the Interior). There hemet Andre, his wife and lifelong companion.Their son Pierre-Louis, who was born in 1956, would also be distinguished by mathemat-

ical talent. This gift earned him the highest mathematical distinction, the Fields Medal,awarded to him during the 1994 International Congress of Mathematicians in Zurich. His par-ents had the great joy of being present for this unique occasion.

CAREER

At the age of 19 years, Jacques-Louis Lions passed the entrance exam to the highly covetedcole Normale Suprieure de la rue dUlm. There he met Bernard Malgrange among others,and at the end of their studies they both decided to opt for a university career in mathematics(a rather uncommon choice at a time when most Normaliens would rather teach the famedclasses de Mathmatiques Spciales in the lyces). They were then awarded a grant by theCNRS (the National Center for Scientific Research) to prepare their doctoral dissertations.And so they both went to Nancy to work under the guidance of a prestigious thesis advisor,Laurent Schwartz, who had just received the Fields Medal for his theory of distributions in1950.

277 2002 The Royal Society

This obituary appeared in theEuropean Mathematical Society Newsletter, and is reproduced with permission.

* On 1 January 2002 this laboratory was renamed Laboratoire Jacques-Louis Lions.




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After defending his thesis in 1954, Lions began his career en province, in other words out-side the Paris region as was then customary, at the University of Nancy, where he held a pro-fessorship from 1954 to 1962.

Far from keeping him fully occupied, his remarkable mathematical achievements duringthat period left him enough time to envisage the immense opportunities offered by scientificcomputing, which was then coming of age, with its many potential industrial applications.This constant quest for applications, which was to guide him all his life and would becomeone of the most exceptional aspects of his career, materialized in 1958 when he became sci-entific consultant for SEMA (the Society for Economics and Applied Mathematics), a societyheaded by Robert Latts, who had entered the cole Normale Suprieure one year after him.Although this kind of inclination is common nowadays, it required courage to follow it at thetime. The applications of mathematics were then far from arousing the enthusiasm that they

now generate!After his time at Nancy, Lions was made a professor at the University of Paris, where hevery quickly instituted a weekly seminar on numerical analysis, a discipline that was practi-cally unheard of in France at that time. This seminar first met in the basement of the InstitutHenri Poincar, then in a dusty room of the Institut Blaise Pascal, which was situated in therue du Maroc in the north of Paris.

When the University of Paris broke into 13 distinct universities, he chose the sixth one,which was to be later named Universit Pierre et Marie Curie. Two of his major initiativesthere were to found the Laboratoire dAnalyse Numrique* (after 30 years on the Jussieu cam-

pus, this department was relocated to the rue du Chevaleret, near Place dItalie, in 1999) andto create a DEA (Diplome dtudes Approfondies, a set of advanced courses that a doctoralstudent has to pass before beginning a dissertation) that specialized in numerical analysis. ThisDEA, from which a considerable number of applied mathematicians now holding positions in

universities, at the CNRS or in industry graduated over the years, was always highly regarded.This degree is now one of the most successful components of the JussieuChevaleretDoctoral School of Mathematical Sciences headed by Yvon Maday.

In 1973, at the early age of 45, Lions had the highly unusual honour of being simultane-ously elected Professor at the celebrated Collge de France and elected to the French Academyof Sciences. At the Collge de France, he held the chair entitled Mathematical Analysis ofSystems and of their Control for 25 years. His series of lectures, which in the tradition of theCollge de France had to be renewed each year, were always followed by vast audiences,attracting not only his own students but also students of his students!

The Seminar of Applied Mathematics that he organized there until 1998, first with JeanLeray and then with Ham Brezis for many years, soon became an institution within an insti-tution. Indeed, countless applied mathematicians, either those in the Paris locality or French

and foreign colleagues happening to be in Paris, gathered each Friday afternoon to hear pres-tigious lecturers such as Stuart Antman, John Ball, Felix Browder, Ciprian Foias, Gu Chao-hao, Li Ta-tsien, Klaus Kirchgssner, Peter Lax, Andrew Majda, Louis Nirenberg, OlgaOleinik, Sergei Sobolev, Tosio Kato and Mark Vishik, among many others.

From 1966 to 1986, Lions was also part-time professor at the cole Polytechnique, wherehe created a course in numerical analysis from scratch that soon became a legend. Followingthe rule at the cole Polytechnique, he also wrote lecture notes; the contents of these were rev-

278 Biographical Memoirs

* On 1 January 2002 this laboratory was renamed Laboratoire Jacques-Louis Lions.




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olutionary for the time, at least in France. Indeed these notes constituted a kind of ency-clopaedia where, with his natural gift for teaching, Lions described and analysed practicallyall that was then known about the numerical analysis of partial differential equations.Introductions to numerical optimization and numerical linear algebra were also presented intwo separate chapters written by his first two doctoral students, Jean Ca and Pierre-ArnaudRaviart. A mystery remains about the first versions of these lecture notes. They were affec-tionately referred to as the Diplodocus, even though no one, including their author, everseemed to understand the reason for this. But all these essentially academic activities, whichwould normally occupy all of ones time, did not take up all of his.

From 1980 to 1984, he was also President of INRIA (National Institute for Research inComputer Science and Automatics), normally a full-time position. His leadership was of pro-found and lasting influence at INRIA: during his first weeks at the head of this institute, he

used his great talents as an organizer to rejuvenate the organization and its objectives, in par-ticular by introducing the notion of project, gathering a clearly identified team around a well-defined objective on a specific theme. During his four-year term, he strongly advocated thecreation of start-up companies by researchers from the Institute and he initialized its decen-tralization through the creation of similar institutes at Sophia-Antipolis and Rennes. Becauseof his personal prestige, the teams he was able to gather, and the numerous first-class interna-tional conferences that he organized there, he greatly contributed to the fame of INRIA.

From 1984 to 1992 he held another high-level, and also normally full-time, official posi-tion as President of the CNES (the National Center for Space Studies), where he continued anddeveloped the action of his predecessor, Hubert Curien, who had just been named Minister ofResearch and Technology. There he used not only his eminent intellectual capacities but alsohis talents for intelligent persuasion to convince the French authorities that the orientations headvocated were well founded. In this way he played a major role in the conception of the

FrenchAmerican TopexPoseidon space programme for oceanography. TopexPoseidon isalso the name of the satellite that made it possible to at last understand El Nio, a major eventin climatology. His influence was likewise a decisive factor in the FrenchRussian negotia-tions that ultimately allowed Jean-Loup Chrtien and Michel Tognini to participate in mannedspace missions.

His presence at the Monday afternoon sances at the French Academy of Sciencesremained rare for many years. But eventually he gave new life to this noble Compagnie (asit is traditionally known among its members) when he became its president in January 1997for the customary two years. Immediately after Lions took office, President Jacques Chiracgave him the mission of supervising the drafting of a document concerning the state of the artworldwide in each of the following areas: access to knowledge for all and electronic pro-cessing of information, knowledge of our planet and ways of life, understanding life systems

and improving health-care for all. He immediately began to work on this ambitious under-taking by creating and heading a Committee 2000, whose task was to analyse the three areasand make proposals, under his continuing close supervision. Remarkably, in spite of the scopeof this project, he was able to meet the 2000 deadline he had set himself. He personally handedPresident Chirac the requested document during a ceremony held at the lyse Palace on 25January 2000. He even succeeded in having all the Members and Corresponding Members ofthe Academy invited for the occasion, which was indeed a first!

However, Lionss actions during his presidency were not limited to Committee 2000. Hisefforts were decisive in promoting the need for a profound reform in the status of the

Jacques-Louis Lions 279




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Academy. The principles of this reform have now been accepted. He also had a major role inthe creation of an Academy of Technology, which had always been desired but never achieved.This academy was eventually created on 12 December 2000.

As exemplified by his presidencies of INRIA and the CNES, Lions was an exceptionallysuccessful promoter of closer ties between academic research, too often seen as disconnectedfrom the real world, and the more pragmatic industrial research. In this spirit, he headed sci-entific committees in major public utility companies, such as Mtorologie Nationale, Gaz deFrance, France Telecom and Electricit de France, and he held high-level advisory positionsin major companies such as Pechiney, Dassault Aviation and Elf.

Lionss influence extended far beyond the frontiers of France. Since the beginning of hiscareer, he was an indefatigable traveller who, in addition to traditional venues in Europe or theAmericas, very quickly added less canonical ones to his list of destinations. For instance, as

early as 1957 he set out for a three-month visit to the Tata Institute of Fundamental Researchin Bombay, which at the time was a genuinely adventurous trip! There he enjoyed the splen-dour of the ancient Taj Mahal Hotel and the hospitality of Kollagunta Gopalaiyer Ramanathan,with whom he contributed to the creation of an applied branch of the Tata Institute on the cam-

pus of the Indian Institute of Sciences in Bangalore 20 years later.In 1966 he began a long series of visits to the (former) Soviet Union. Often invited by the

USSR Academy of Sciences or by the Novosibirsk Institute for Computation, he initiatedmany scientific exchanges with eminent Soviet mathematicians such as Guri Marchuk, OlgaOleinik, Lev Semenovitch Pontryagin, Ilia Vekua, Mark Visik and Nicolay NicolayevichYanenko. One of his achievements during this period, and not the least, was to contributegreatly to the dissemination of Soviet research in applied mathematics among Western scien-tists.

A trip that left him with a lasting impression was the journey that he undertook in 1975 to

Beijing, where he was received with great ceremony. There he was particularly impressed bythe mathematical talents of Feng Kang, who had just independently rediscovered the finite-element method. He was also impressed by Feng Kangs impetuosity when he spoke about theGang of Four!

However, his international ventures were not limited to traditional scientific exchanges: histalents as a lecturer, thesis adviser and organizer produced many disciples throughout thecountries he visited. As early as the 1960s, for instance, he was the adviser to Antonio Valle,the first in a long series of students from Spain and Portugal, who in turn set up numericalanalysis departments at the Universities of Malaga, Sevilla, Santiago de Compostela andLisboa and at the Universidad Complutense de Madrid, modelled on the one he had created inParis. In the same vein, in 1997 he was the main speaker in a European video conference onMathematics and the Environment, organized in Madrid by Jesus Ildefonso Diaz. He also

chaired the committee awarding the 10 Prizes for Young Mathematicians during the ThirdEuropean Congress of Mathematics held in Barcelona in 2000. He also chaired the ScientificCommittee of the Istituto di Analisi Numerica del CNR of the Univerity of Pavia, which washeaded for several decades by Enrico Magenes and then by Franco Brezzi.

Together with Paul Germain, Lions represented France at the 1975 meeting on FunctionalAnalysis and Mechanics of IUTAM (the International Union for Theoretical and AppliedMechanics) held in Luminy, where the other representatives were Klaus Kirchgssner for WestGermany, Sir James Lighthill, F.R.S., for the UK, and William Prager for the USA.

However, his intelligent proselytizing was not limited to Europe. In China, for instance, he





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was one of the driving forces behind the creation in 1997 of LIAMA (the FrenchChineseLaboratory of Computer Science, Automatics, and Applied Mathematics), an offspring ofINRIA and the Academia Sinica, housed since then in Beijing by the Institute of Automaticsof the Academy of Sciences. He likewise had a major role in the creation in 1998 of ISFMA(the ChineseFrench Institute of Applied Mathematics), splendidly housed by the Departmentof Mathematics of Fudan University in Shanghai, thanks to the tireless efforts of its Director,Li Ta-tsien.

Lions was President of the IMU (International Mathematical Union) from 1991 to 1995.During a meeting of this organization in Rio de Janeiro on 6 May 1992, he proposed that theyear 2000 be designated World Mathematical Year. This proposal, which was later supported

by UNESCO, turned out to be a genuine success story that significantly contributed to theimprovement of the image of mathematics among the general public and helped to encourage

mathematical research in developing countries.He was also a constant supporter of the initiatives of the Third World Academy of Sciences(TWAS), either directly or through colleagues from his group. Particularly noteworthy in thisrespect were his undertakings for the progress of mathematical research in Africa.

SCIENTIFIC WORK

The mathematical output of Jacques-Louis Lions was immense. Alone or in collaboration, hewrote more than 20 books; most have become classics, often being translated into several for-eign languages. He also wrote more than 500 papers. The different themes of his work are

briefly described below, in an order that approximately follows their chronology.He had, and will long continue to have, a considerable influence on mathematics and its

applications, not only through his own work but also through that of the School that he cre-ated and constantly kept in touch with. This School, which numbers some 50 initial studentsand scores of students of students, has acquired a widespread fame over the years, not only inuniversity circles but also in industry, an accurate indication that the directions of research heenvisioned and promoted were highly relevant.

If a single title were to be attached to Lionss mathematical works, it might be with a fairdegree of accuracy Partial differential equations in all their aspects: existence, uniqueness,regularity, control, homogenization, numerical analysis, etc., and the applications they model,such as fluid and solid mechanics, oceanography, climatology, etc..

Lions produced his first mathematical work in 1951. At the same time two major bookswere published, one by Laurent Schwartz on the theory of distributions and one by SergeiSobolev on their applications to mathematical physics, as well as a seminal paper by John von

Neumann and Robert Richtmyer on the numerical approximation of nonlinear hyperbolicproblems arising in hydrodynamics.Inspired by these works, Lionss first objectives were to undertake a systematic study of

linear and nonlinear boundary-value problems, notably by constantly using the theory of dis-tributions, and then to find ways to approximate their solutions numerically.

In 1954 he began a series of collaborations and lasting friendships with eminent Italianmathematicians such as Enrico Magenes, Guido Stampacchia, Ennio de Giorgi and GiovanniProdi (brother of the current President of the European Union). One such collaborationresulted in an exhaustive analysis of linear boundary-value problems posed in fractional





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Sobolev spaces, thanks in particular to the theory of interpolation between Banach spaces thathe initiated with Jack Peetre in 1961. This analysis is the subject of the celebrated three-vol-ume treatiseNon-homogeneous boundary value problems and applications (19681970) thathe wrote with Enrico Magenes. From 1965 to 1967 he also developed with Guido Stampacchiathe foundations of the theory of variational inequalities, as they appear for instance in unilat-eral problems in elasticity.

His inclination for applications led him to propose a particularly elegant proof of Kornsinequality, based notably on a fundamental result in distribution theory known as Lionsslemma (although several other results of his bear the same name). He further developed appli-cations of the theory of variational equations or inequalities to mechanics by mathematicallyanalysing Bingham fluid, friction, viscoelasticity or plasticity models. These applications arethe substance of another well-known book, Inequalities in mechanics and physics (1972),

which he wrote with Georges Duvaut.He was equally interested in the numerical simulation of these problems, at a time when itwas realized that the applicability of finite-difference methods had reached its limits. Forinstance, these methods do not perform well when the problems to be approximated have rap-idly varying coefficients or are posed on domains with complicated geometries. In contrast,the finite element method, already familiar to engineers handling these types of difficulty,remained essentially unknown to mathematicians.

With a remarkable intuition, Lions immediately foresaw that it was preferable to discretizethe variational, or weak, formulations of boundary-value problems containing partial differ-ential equations rather than the partial differential equations themselves. Accordingly, hequickly pointed out to his group of colleagues and students the interest of studying andanalysing Galerkin methods in general and finite-element methods in particular. A quite pro-ductive period ensued, to which he himself contributed with another classic,Numerical analy-

sis of variational inequalities (1976), co-authored with Roland Glowinski and RaymondTrmolires.

His bookQuelques mthodes de rsolution de problmes aux limites non linaires (1969)(Some methods for solving nonlinear boundary-value problems) is a major contribution to thetheory of nonlinear partial differential equations, which remains a substantial source of inspi-ration (it is unfortunate that this book was never translated into English). In this work, Lionsintroduced and systematically analysed the so-called compactness methods, which have a keyrole in the existence theory for the NavierStokes and von Krmn equations, the monotonymethods he had developed with Jean Leray, and the regularization and penalty methods, whichcan for instance be applied to the Schrdinger or Kortewegde Vries equations. For the most

part, the results found in this book are due either to himself or to his students, in particularHam Brezis and Luc Tartar.

Most of the works mentioned so far, together with many generalizations that they led to,were to be assembled in the monumental treatiseMathematical analysis and numerical meth-ods for science and technology (198485), conceived and edited by Lions and Robert Dautray.This work, which contains almost 4000 pages, is justly regarded as the modern counterpart ofthe celebratedMethods of mathematical physicsby Richard Courant and David Hilbert.

His continuing interest in problems with small parameters led him to write Singular pertur-bations in boundary value problems and in optimal control(1973), a book in which he laid downthe foundations of the asymptotic analysis of such problems. The methods and notions that hethen introduced and analysed, such as a priori estimates, stiff problems, boundary layers and





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multiple scales, were subsequently recognized as fundamental to many applications. Forinstance, they later had a major role in the mathematical modelling of elastic structures, ormulti-structures, made of plates, rods or shells.

Another field in which small parameters naturally arise is the modelling of composite mate-rials, which are used constantly in the aerospace industry for example. Their asymptotic analy-sis, which is a special case of what became known as homogenization theory, was abundantlydeveloped and illustrated by applications in another seminal work, Asymptotic analysis forperiodic structures (1978), which he wrote with Alain Bensoussan and George Papanicolaou.In this book, a substantial number of essentially empirical formulae used in the modelling of

periodic structures were rigorously justified for the first time, thanks notably to the compen-sated compactness method due to his students Francois Murat and Luc Tartar and to the oscil-lating test-functions method of Luc Tartar.

A fundamental study by Lev Semenovitch Pontryagin about the optimal control of systemsgoverned by ordinary differential equations (the objective was to control the trajectories ofartificial satellites) immediately attracted his attention in 1958. Through his existing contactswith the engineering community, he quickly became convinced that the next step was toextend optimal control to distributed systems, that is, systems whose state is governed by par-tial differential equations. The inclination that he then developed for the optimal control ofsuch systems was subsequently to remain at the centre of his mathematical interests.

A pioneer as always, he began by laying down the foundations of a general theory in yetanother celebrated book, Optimal control of systems governed by partial differential equations(1968), in which he notably introduced an infinite-dimensional version of the Riccati equation.

In two books co-authored with Alain Bensoussan, Applications of variational inequalitiesto stochastic control(1978) andImpulse control and variational inequalities (1982), he con-tinued his investigations by considering in particular the optimal control of systems that are

not necessarily well posed or that have multiple states.After having so thoroughly analysed the main aspects of optimal control theory, Lions

shifted his interests to the study of controllability, a discipline that in essence seeks to answerthe following type of question: given a system in an arbitrary initial state, is there a way of act-ing on it in such a way that its solution reaches a given final state in a finite time, for instance

by imposing adequate boundary conditions?During the prestigious John von Neumann Lecture that he gave at the Society for Industrial

and Applied Mathematics (SIAM) Congress in Boston in 1986, he presented for the first timehis now-famous HUM (Hilbert uniqueness method) for the exact controllability of linear time-dependent equations. He chose this particular terminology to emphasize the fact that the fea-sibility of such controllability is related in an essential way to the uniqueness of the solutionto the adjoint problem, typically obtained by the Holmgren or the Carleman theorem.

This lecture was the starting point of numerous publications by himself or his School. Inparticular, he began by publishing no less than three books on the subject in the same year,Contrlabilit exacte, perturbations et stabilisation de systmes distribus (Exact controlla-bility, perturbations and stabilization of distributed systems) in two volumes (1988) and, withJohn Lagnese,Modelling, analysis, and control of thin plates (1988), which contains an abun-dance of applications to the theory of elastic plates. In 1995 he also established with EnriqueZuazua the generic character of the controllability of the three-dimensional Stokes equations:if there is no approximate controllability for a given open set, it is always possible to findanother arbitrarily close open set for which this type of controllability holds.





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These works constituted yet another mark of his constant interest in real-life applications.He was also concerned to propose numerically feasible approximation methods. These werethe theme of a very long article co-authored with Roland Glowinski, an article so long that itsnearly 300 pages took up two consecutive issues ofActa numerica (199495).

Even though the most recent researches of Lions were in different areas, they continued tobe partly influenced by the methodology he had developed for questions of controllability.

In 1990, he started to express his great interest in climatology inEl Planeta Tierra. In thisbook, which was directly published in Spanish, he described in a masterly fashion and in aremarkably accessible style the most important problems originating in this science, such asmodelling, numerical simulation and sensitivity to initial conditions. From 1994 to 1998 hiscourses at the Collge de France were all about these subjects. The models found in climatol-ogy include complex systems of partial differential equations such as those of NavierStokes

or of thermodynamics. However, these systems had never been seriously analysed from amathematical viewpoint, although they had been routinely used in a massive way since the1960s for numerical simulation in weather forecasting.

In spite of the truly diabolical complexity (as he was fond of saying) of the combinationof partial differential equations, boundary conditions, transmission conditions, nonlinearities,

physical assumptions and so on that enter these models, Lions, together with Roger Temamand Shouhong Wang, was able to study questions of existence and uniqueness of solutions, toestablish the existence of attractors and to propose numerical methods. He even succeeded inteaching this work on a blackboard, a pedagogical tour de force!

In 1995, he began with Evariste Sanchez-Palencia another series of studies in which theydeveloped the theory of sensitive problems, exemplified by the boundary-value problems thatappear in the theory of linearly elastic membrane shells. In such problems, which in a senseare the antithesis of well-posed problems, arbitrarily small, yet arbitrarily smooth, changes in

the right-hand sides of the equations can induce sudden changes on the properties of theirsolutions. It is perhaps no coincidence that the analysis of such problems relies in particularon uniqueness theorems that bear a resemblance to those needed in the HUM.

In 1997, Lions returned to the numerical analysis of parallel algorithms and domain decom-position methods in a long series ofnotes to Comptes Rendus de lAcadmie des Sciences, usu-ally co-authored with Olivier Pironneau and published from 1997 to 2001. In fact, these kindsof topic had been on his mind for a long time: as early as the 1980s he had been an ardentadvocate of installing a parallel computer at INRIA. The main idea in these notes was to intro-duce parallelism in the continuous problem rather than in the discrete one, an approach that isin fact quite general because it applies equally well to any problem that is approximated by aniterative method, such as a fractional step method, a decomposition method into sub-problemsin optimization theory or a domain decomposition method.

One can only be impressed by these immense contributions, both by the quality, diversityand novelty of the mathematics used and by the permanent quest for new applications that hadpreviously been believed to be inaccessible.

Like John von Neumann, whom he deeply admired, Lions was a visionary who veryquickly understood that the availability of ever-increasing computational power could revolu-tionize the modelling of phenomena and could thereby improve our knowledge and masteryof the physical world, provided that the required mathematics was simultaneously created anddeveloped. He contributed admirably to this latter task.





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HONOURSLions justly received numerous honours. Although he always remained modest about them,their list is truly astonishing: He was a Commander of the French Legion of Honour and aGreat Officer of the French National Order of Merit, a distinction he received at the hands ofPresident Chirac on 23 February 1999. He was a member of 22 foreign academies andreceived honorary doctorates from 19 universities; he received the most prestigious prizes andhe delivered the most coveted lectures.

He was in particular awarded three prizes by the French Academy of Sciences and in addi-tion the John von Neumann Prize in 1986, the Harvey Prize from the Technion in 1991 and theLagrange Prize at the International Congress in Industrial and Applied Mathematics (ICIAM)meeting in Edinburgh in 1999. Lions was proud to have had the rare honour of having shakenthe hand of Emperor Akihito on receiving the highly prestigious Japan Prize in 1991. It was the

climax of a perfectly and meticulously organized week, which had particularly impressed him!In particular, he was three times an invited speaker at an International Congress of

Mathematicians, in 1958, 1970 and 1974. He gave the John von Neumann Lecture at theSIAM meeting in Boston in 1986. He was a plenary speaker at the ICIAM Congress inHamburg and at the SIAM Congress in Philadelphia in 1995, and he held the Galileo Chair atthe University of Pisa in 1996. He also had the extremely rare honour for a scientist, especiallyfor a mathematician, of speaking before a parliament! More specifically, he delivered anaddress entitled Will it ever be possible to describe, understand, and control the inanimate andanimate world by means of the languages of mathematics and informatics? in front of theCortes, which had specially gathered in Madrid on 21 January 2000 for the occasion, as partof the celebrations of World Mathematical Year 2000.

He belonged to the most famous academies, such as the USSR Academy of Sciences and

the American Academy of Arts and Sciences, to which he was elected in 1982 and 1986,respectively. In 1996 he was simultaneously elected to the Foreign Membership of The RoyalSociety, to the National Academy of Sciences of the USA and to the Third World Academy ofSciences, two years before being simultaneously elected to the Academia Sinica and to theAccademia Nazionale dei Lincei in Rome. The Pontifical Academy of Sciences, to which hewas elected in 1990, seemed to be particularly dear to him. It might perhaps be not as wellknown as other bodies, but it is an unusually rare honour to become one of its members!

THE MAN

Who was the man behind all these endeavours? What I knew of him convinced me that bothhis human and professional qualities were truly exceptional.

Lions wrote abundantly, very rapidly, and with an astonishing ease not only mathematicsbut also countless letters, which were his favourite means of communication. He was a mas-ter with the fax, which he used with an amazing efficiency. For instance, it was not uncom-mon for each of his various collaborators at any given time to receive four or five faxes aweek, sometimes of up to 30 pages if their contents were mathematical.

Even though he wrote abundantly, he confessed that he did not usually keep track of hismany letters, perhaps because he could rely entirely on his memory, or perhaps because he pre-ferred to spare himself a Herculean archival task. Let us hope that his correspondents had thegood sense to keep his letters, which could thus be compiled later.





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By any measure, his abilities were astounding. For instance, he once told me that it tookhim only a few weeks to write the several hundred pages of the Diplodocus lecture notesmentioned earlier. Similarly, his indifference to a lack of sleep or to the most extreme jetlagand his freshness after lengthy flights were always a subject of astonishment among his trav-elling companions.

As John Ball put it so well, Jacques-Louis Lions was a man of considerable personal mag-netism and charm, whose charisma, brilliance as a teacher, and accessibility attracted others towork with him. And indeed it was obvious that Lions had an ample share of charisma, evenif charisma is not easy to define rigorously! He was also incredibly open and displayed suchamiable and simple manners that any one of his current students or collaborators felt they werethe centre of his attention.

He was also very brave in the face of physical danger and suffering. Even when the pain

became unbearable, he never complained, keeping on the contrary his compassion for others.All those who met him will cherish the memory of his warm personality, the vision that heconveyed so well, and his profound intelligence.

BIBLIOGRAPHY

BooksLectures on elliptic partial differential equations (1957). Bombay: Tata Institute.quations diffrentielles oprationnelles et problmes aux limites (1961). Berlin: Springer-Verlag.Problmes aux limites dans les quations aux drives partielles (1962). Montral University Press.(With R. Latts) Mthodes de quasi-rversibilit et applications (1967). Paris: Dunod. (English translation: Quasi-

reversibility methods and applications, Elsevier, New York (1969). Russian translation published by Mir,Moscow (1970).)

Contrle optimal de systmes gouverns par des quations aux drives partielles (1968). Paris: Dunod. (Englishtranslation: Optimal control of systems governed by partial differential equations , Springer-Verlag, Berlin(1970). Russian translation published by Mir, Moscow (1972).)

(With E. Magenes)Problmes aux limites non homognes et applications (three volumes, 196870). Paris: Dunod.(English translation: Non-homogeneous boundary-value problems and applications, Springer-Verlag, Berlin(three volumes, 197273). Russian translation published by Mir, Moscow (1971).)

Quelques mthodes de rsolution des problmes aux limites non linaires (1969). Paris: Dunod. (Russian translationpublished by Mir, Moscow (1972).)

(With G. Duvaut) Les inquations en mcanique et en physique (1972). Paris: Dunod. (English translation:Inequalities in mechanics and physics, Springer-Verlag, Berlin (1976). Russian translation published byNauka, Moscow (1980).)

Some aspects of the optimal control of distributed parameter systems. Proceedings of CBMS Conference No. 6,SIAM, Philadelphia, 1972.

Sur le contrle optimal des systmes distribus. Monographie no. 20 (1973). Genve: Enseignement Mathmatique.

(Russian translation (1973).)Perturbations singulires dans les problmes aux limites et en contrle optimal. Lecture notes in mathematics, vol.

323 (1973). Berlin: Springer-Verlag.(With R. Glowinski & R. Trmolires) Analyse numrique des inquations variationnelles (two volumes, 1976).

Paris: Dunod. (English translation:Numerical analysis of variational inequalities, North-Holland, Amsterdam(1981).)

Sur quelques questions danalyse, de mcanique et de contrle optimal(1976). Montral University Press.(With A. Bensoussan) Applications des inquations variationnelles au contrle stochastique (1978). Paris: Dunod.

(English translation:Applications of variational inequalities to stochastic control, North-Holland, Amsterdam(1982).)





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(With A. Bensoussan & G. Papanicolaou) Asymptotic analysis for periodic structures (1978). Amsterdam: North-Holland.

Some methods in the mathematical analysis of systems and their control(1981). Beijing: Science Press; New York:Gordon & Breach.

(With A. Bensoussan) Contrle impulsionnel et inquations variationnelles (1982). Paris: Gauthier-Villars. (Englishtranslation:Impulse control and variational inequalities, Heyden & Son, Philadelphia (1984).)

Contrle des systmes distribus singuliers (1983). Paris: Gauthier-Villars. (Russian translation published by Nauka,Moscow (1987).)

(With R. Dautray) Analyse mathmatique et calcul numrique pour les sciences et les techniques (three volumes,19841988). Paris: Masson. (English translation:Mathematical analysis and numerical methods for scienceand technology, Springer-Verlag, Berlin (nine volumes, 198893).)

Contrlabilit exacte, perturbations et stabilisation de systmes distribus (two volumes, 1988). Paris: Masson.(With J. Lagnese)Modelling, analysis and control of thin plates (1988). Paris: Masson. [Not translated into French.]El Planeta Tierra (1990). Madrid: Instituto de Espaa, Espasa-Calpe.

Sentinelles pour les systmes distribus donnes incompltes (1992). Paris: Masson.(With R. Temam & S. Wang) Models for the coupled atmosphere and ocean. Computational Mechanics Advances,vol. 1 (1993). Amsterdam: North-Holland.

Series edited by Lions(With H. Fujita, H. B. Keller & G. Papanicolaou) Studies in mathematics and its applications (30 volumes,

19762001). Amsterdam: North-Holland.(With H. Brezis)Nonlinear partial differential equations and their applications. Collge de France seminar(12 vol-

umes, 198194). Harlow: Pitman-Longman.(With P. G. Ciarlet)Mathmatiques appliques pour la matrise (21 volumes, 198297). Paris: Masson.(With P. G. Ciarlet)Recherches en mathmatiques appliques (42 volumes, 198597). Paris: Masson.(With P. G. Ciarlet)Handbook of numerical analysis (seven volumes, 19902000). Amsterdam: North-Holland.(With D. Cioranescu)Nonlinear partial differential equations and their applications. Collge de France seminar(two

volumes, 19982001). Harlow: Pitman.

Books dedicated to LionsAnalyse mathmatique et applications. Contributions en lhonneur de Jacques-Louis Lions (1988). Montrouge:

Gauthier-Villars.Frontiers in pure and applied mathematics. A collection of papers dedicated to Jacques-Louis Lions on the occasion

of his sixtieth birthday (1991) (ed. R. Dautray). Amsterdam: North-Holland.quations aux drives partielles et applications. Articles ddis Jacques-Louis Lions (1998). Paris: Gauthier-

Villars.





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