Sergei Lvovich Sobolev

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Sergei Lvovič Sobolev ( Russian Сергей Львович Соболев , scientific transliteration Sergej Lʹvovič Sobolev ; born October 6, 1908 in Saint Petersburg , † January 3, 1989 in Moscow ) was a Soviet mathematician who mainly dealt with partial differential equations and numerical equations .

Sobolev 1970

Live and act

Sobolev was the son of a lawyer (with ancestors among the Siberian Cossacks), but he died when Sobolev was still a child. He was raised by his mother, who was a teacher at the Medical Institute in Petrograd . During the civil war he lived with his mother in Kharkov and did not move to Petrograd again until 1923. He began to study mathematics at the University of Leningrad in 1925 with Nikolai Maximowitsch Günter , Smirnow and Fichtenholz, among others . In 1929 he finished his studies and taught at the Seismological and Electrotechnical Institute in Leningrad. At the same time he published work on partial differential equations. In 1932, Winogradov brought him to the Steklov Institute (which was then still in Leningrad), where he worked with Smirnov on, among other things, differential equations of elasticity theory (he solved Horace Lamb's problem on wave solutions in the elastic half-space) and the theory of diffraction.

In 1934 he moved to Moscow with the Steklow Institute , where he headed the differential equations department from 1935. At the same time he was from 1935 to 1957 professor at Lomonosov University . During the Second World War he was director of the Steklov Institute, which was temporarily evacuated to Kazan . During this time he worked under Kurchatov in the Soviet atomic bomb project - with IK Kikoin he was responsible for the development and industrial technical implementation of uranium isotope enrichment in gas diffusion systems. He was also the main assistant of Kurchatov in Laboratory 2. In addition, he still found time to write his main work on functional analysis at LIPAN (as Kurchatov's Laboratory 2 was called after 1949). He also dealt with numerical studies on the dynamic behavior of nuclear reactors. During this time, Sobolev was not allowed to have any foreign contacts. His involvement in the Soviet nuclear engineering program was a major reason why he could not continue his research on generalized functions from the 1930s, while in France Laurent Schwartz developed the theory in the late 1940s and in the West was considered the father of the theory of distributions.

After the Second World War he continued his turn to numerical mathematics and headed the numerical mathematics department at Lomonosov University from 1952 to 1960. From 1956 he was the founding director of the Mathematical Institute of the Siberian Department of the Soviet Academy of Sciences in Novosibirsk / Akademgorodok and also from 1960 to 1978 professor at the University of Novosibirsk .

In 1933 he became a corresponding member and in 1939 a full member of the Soviet Academy of Sciences . He was also a member of the Académie des sciences in Paris and the Accademia dei Lincei and, since 1963, an honorary member ( Honorary Fellow ) of the Royal Society of Edinburgh . In 1941 he received the Stalin Prize . He also received three Soviet state awards and in 1988 the Lomonosov Gold Medal of the Soviet Academy of Sciences. In 1951 he became a hero of socialist labor . In 1966 he was invited speaker at the International Congress of Mathematicians (ICM) in Moscow (theory of the approximation of the integrals of functions of several variables) and in 1962 in Stockholm (Quelques questions de la théorie des intégrations numériques et de lʹinterpolation pour les fonctions de plusieurs variables indépendantes; Les formules de lʹintégration numérique sur la surface de sphère).

In the 1930s he worked at the Steklow Institute , introduced the Sobolev spaces and proved norm estimates for embedding sentences . He introduced (influenced, among other things, by studies by Jacques Hadamard ) in the mid-1930s generalized functions (called by Schwartz distributions ), initially in studies of the wave equation. He lectured on this at the second Soviet mathematicians' congress in 1934 and published two important papers in 1935 and 1936. The work was known to French mathematicians such as Hadamard (who regularly visited the Soviet Union and, for example, met Sobolev in 1930) and Jean Leray, and Schwartz knew them too.

From the 1940s he turned to numerical mathematics, in particular the numerical quadrature of multi-dimensional functions.

Vera Nikolaevna Maslennikova was an employee of Sobolev.

Fonts

  • Some applications of functional analysis on equations of mathematical physics, Berlin, Akademie Verlag 1964, (Russian original 1950, English translation American Mathematical Society 1963)
  • Cubature formulas and modern analysis, Gordon and Breach 1992
  • with V. Vaskevich: The theory of cubature formulas, Kluwer 1997
  • Imbedding theorems, American Mathematical Society Translations Series, 1970
  • On a boundary value problem for polyharmonic equations, American Mathematical Society Translations Series, 1963
  • Selected Works, 2 volumes, Springer 2006 (editors Gennadi Demidenko, Vladimir Vaskevich).
  • Méthode nouvelle à résoudre le sondème de Cauchy pour les équations linéaires hyperboliques normales, Matematicheskii Sbornik, Vol. 1, 1936, pp. 39–72, Online (French, introduction of distributions)
  • Sur un théorème dʹanalyse fonctionnelle (Russian with French summary), Matematicheskii Sbornik, Vol. 4, 1938, pp. 471–497 (Sobolew's embedding theorem)

literature

Web links

Individual evidence

  1. ↑ Kantor, Mathematical Intelligencer 2004, No. 1, see literature
  2. ↑ Laurent Schwartz: Theory of distributions , Hermann, Paris 1950, 1951
  3. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. (PDF file) Royal Society of Edinburgh, accessed April 10, 2020 .
  4. ↑ The Cauchy Problem in the Space of Functions , Doklady Akad. Nauk (Negotiations of the Russian Academy of Sciences), 1935, Volume III (in Russian), New Methods for Solving the Cauchy Problem of Normal Hyperbolic Linear Equations , Mat. Sbornik, 1936 , Volume 1, pp. 39-72 (in French)
  5. ↑ Kantor, Math. Intelligencer 2004, No. 1, p. 42. Leray informed Sobolev in the 1980s that he was discussing Sobolev's article from 1936 before the Second World War with Schwartz. Schwartz himself states that he did not know about it before 1945, Lützen: The Prehistory of distribution theory , 1980, p. 67
personal data
SURNAME Sobolew, Sergei Lvowitsch
ALTERNATIVE NAMES Соболев, Сергей Львович (Russian)
BRIEF DESCRIPTION Soviet mathematician
DATE OF BIRTH October 6, 1908
PLACE OF BIRTH Saint Petersburg , Russian Empire
DATE OF DEATH January 3, 1989
Place of death Moscow , RSFSR , Soviet Union