Lopatynsky, Yaroslav B.
Lopatynsky, Yaroslav B. [Лопатинський, Ярослав; Lopatyns'kyj, Jaroslav], b 9 November 1906 in Tbilisi, Georgia, d 10 March 1981 in Donetsk. Ukrainian mathematician; full member of the Academy of Sciences of the Ukrainian SSR from 1965. Lopatynsky graduated from Azerbaidzhan University in 1926. He taught at institutions of higher learning in Baku, and in 1945–63 he held a chair in differential equations at Lviv University. After working two years at Moscow’s Industrial Institute, in 1966 Lopatynsky became head of the Section of Partial Differential Equations at the Institute of Applied Mathematics and Mechanics of the Academy of Sciences of the Ukrainian SSR in Donetsk. Most of his basic research was devoted to the development of the theory of linear and nonlinear partial differential equations. During his Lviv period Lopatynsky obtained important results in the theory of systems of elliptic linear equations, for which he constructed local fundamental solutions. He also developed a method of reducing general boundary value problems to regular integral equations. Lopatynsky was the first person to formulate a condition on the relation between the coefficients of the system and the coefficients of the boundary operators which is necessary and sufficient for the normal solvability of boundary value problems. This is now known as the Lopatynsky Condition. He also obtained some basic results in the solvability of the Cauchy problem for operator equations in Banach spaces (see Stefan Banach). In addition to his scientific articles Lopatynsky wrote Introduction to the Contemporary Theory of Partial Differential Equations (1980).
[This article originally appeared in the Encyclopedia of Ukraine, vol. 3 (1993).]