Sobolev, Sergei L’Vovich
Born Sept. 23 (Oct. 6), 1908, in St. Petersburg. Soviet mathematician and engineer. Academician of the Academy of Sciences of the USSR (1939; corresponding member, 1933); Hero of Socialist Labor (1968). Member of the Communist Party of the USSR since 1940.
After graduating from Leningrad State University in 1929, Sobolev was a staff member of the Institute of Seismology of the Academy of Sciences of the USSR. From 1932 to 1943 he was affiliated with the V. A. Steklov Institute of Mathematics of the Academy of Sciences of the USSR. Sobolev was a professor at Moscow State University between 1935 and 1957. From 1943 to 1957 he was on the staff of the Institute of Atomic Energy. In 1957 he became a professor at the University of Novosibirsk and was made director of the Institute of Mathematics of the Siberian Division of the Academy of Sciences of the USSR.
Sobolev proposed a new method for solving hyperbolic partial differential equations. In collaboration with V. I. Smirnov, he developed a method of functionally invariant solutions for dynamic problems of waves in stratified media. He initiated the systematic application of functional analysis to the theory of partial differential equations. Sobolev introduced a class of function spaces that was later named after him, and he studied the imbedding relations for the spaces. He developed concepts of generalized solutions of partial differential equations and, in 1935, presented the first rigorous definition of generalized functions. He used these concepts to study some boundary value problems of partial differential equations. In computer mathematics, Sobolev introduced the concept of the closure of computer algorithms and provided a precise estimate of the bounds of the error in cubature formulas.
Sobolev received the State Prize of the USSR in 1941, 1951, and 1953. He has been awarded seven Orders of Lenin, two other orders, and several medals.
WORKSUravneniia matematicheskoifiziki, 4th ed. Moscow, 1966.
Nekotorye primeneniia funktsional’nogo analiza v matematicheskoi fizike, 2nd ed. Novosibirsk, 1962.
Vvedenie v teoriiu kubaturnykh formuL Moscow, 1974.