A N D R E I V A S I L ' E V I C H B I T S A D Z E ( O n His 5 0 t h B i r t h d a y )

L. V. K a n t o r o v i c h

A well-known Soviet Mathematician and Corresponding Member of the Academy of Sciences of the USSR, Andrei Vasil 'evich Bitsadze, celebrated his 50th birthday on lvlay 52, 1966.

His career starts very early. Already at the age of 16 he is working as a mathematics and physics master in lower secondary schools in the Chiaturskii region of the Republic of Georgia. He graduates with distinction fror~ the Tbilisskii University in 1940, and starts work as a research assistant at the Tbilisskii Institute of Mathematics of the Academy of Sciences of the Georgian Republic.

In 1945 Andrei Vasil 'evich defends the Candidate's thesis and in 1951 he defends his .Ph.D. thes is ,havingcom- pleted it at the V. A. Steklov Mathematics Institute of the Academy of Sciences of USSR. In 1958 he is elected Corresponding Member of the Academy of Sciences of the USSR, and in 1959 he begins his permanent work at the Siberian Branch of the Academy of Sciences of USSR.

His first scientific work was on the theory of elasticity. In particular, he reduced to quadratures the solution of the generalized Hertz problem on local deformations arising under compression of two two-dimensional elastic bodies.

The work of A. V. Bitsadze is mainly concerned with the theory of boundary problems of elliptic equations and systems. He found a general representation for all regular solutions fbr one sufficiently general class of systems of equations of the second order of an elliptic type with analytic coefficients which enabled him to study boundary problems (of Dirichtet, Neumann, and Poincare). The absence of Fredholm alternatives is, as a rule, a character- istic feature of these problems. By reducing them to equivalent singular equations, it was possible to formulate theorems characterizing, in one way or another, the solvability of the problems in question. These works border upon the well-known investigations of I. N. Bekua.

It was not known until A. V. Bitsadze's work was published, even in the case of Dirichlet problems, ~?t~ether uniform ellipticity of the system ensures that Fredholm alternatives are present. Andrei VasiI 'evich was first to con- sl~uct examples of second-order systems whose ellipticity in the sense of Petrovskii is not sufficient even for the normal

solvability in the sense of Hansdorff of the Dirichtet bound ary-vatue pt oblem.

These examples have played an important role: on the one hand they have stressed the fact that one must find stronger conditions to ensure normal solvability of bounda~-value problems in some sense (say, strong etlipticity in the sense of Vishik, weak connectivity of Bitsadze, or the Shapiro-Lopatin- skii condition); on the other hand, they have given rise to little-investigated linear problems which have no normal solution either in the sense of Noether or Hansdorff.

In the second series of publicatiom Andrei Vasil 'evich d e a l with mixed- type equations.

It was A. V. Bitsadze who first investigated a number of boundary-value problems (Triconi-type problem, Frankel' problem, and others) for a typical mixed-type equation proposed by M. A~ Lavrent'ev. It was very difficult to investigate these problems by employing known methods. Andrei Vasil 'evich developed a new, delicate, mathemat ica l apparatus by combining the methods of the theory of functions of singular integral equations and of partial differ- ential equations. The developed methods enabled him to make considerable progress in the analysis of the mixed-type equation. The result of these fun- damental investigations is the well-known monograph of Andrei Vasil 'evich "Equations of the Mixed Type" published in 1959 and, subsequently, translated into foreign languages.

ANDREI VASIL'EVICH BITSADZE

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 4, pp. 729-730, July-August, 1966.

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The series also includes investigations of mixed- type equations in mul t id imens ional domains and equations of the mixed -compos i t e type which had not been much investigated. Although a number of mathemat ic ians have now been working on them, the results obtained by Andrei Vas t rev ich are s t i l l very valuable .

Side by side with his study of par t ia l d i f ferent ia l equations, Andrei Vasi l 'evich was also much and successfully engaged in studying the theory of mul t id imens ional singular equations. In this l i t t l e - inves t iga t ed field, he also suc-

ceeded in obta in ing many interest ing results.

In his recen t scient i f ic work he has concentra ted on the problem of d i rec t ional derivat ive in space. It may

be ment ioned that the approach used in the investigations in the planar case is not suitable in the case of higher

dimensions,

I t was Andrei VasiI 'evich who first established theorems on the exis tence and number of solutions for problems with d i rec t iona l der ivat ive in th ree -d imens iona l space, as dependent on the structure of the set in which the vector

of the di rect ion of the der ivat ive of the required function is posit ioned in the tangent plane.

He has managed remarkedly well to combine his strenuous research work with teaching and social duties. He

has sat on the Commi t t ee for Awarding State Prizes, on the National Commit tee of Soviet Mathemat ic ians ,and has

been a member of the Higher Cer t i f ica te Commission.

His organiza t ional abi l i t ies have found an exce l l en t out le t in his work at the Siberian Section of the Academy

of Sciences of the USSR.

Andrei Vas i r ev ich was the head of the Theory of Functions Sect ion of the Mathematics Institute of the

Siberian Sect ion of the Academy of Sciences of the USSR, and held the Chair of the Theory of Functions at the Novosibirsk University; he has also been University (Communist) Party leader for several years.

A. V. Bitsadze has made an important contribution to the organiza t ion and further deve lopment of a new

scient i f ic center.

Full of vigor and creat ive energy, A. V. 8itsadze ce lebra tes his 50th bir thday by publishing a b i g new work,

a monograph on the theory of boundary-value problems for e l l ip t i c equations.

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