Nicolai V. Krylov


Nicolai Vladimirovich Krylov is a Russian mathematician specializing in partial differential equations, particularly stochastic partial differential equations and diffusion processes. Krylov studied at Lomonosov University, where he in 1966 under E. B. Dynkin attained a doctoral candidate title and in 1973 a Russian doctoral degree. He taught from 1966 to 1990 at the Lomonosov University and is since 1990 a professor at the University of Minnesota. At the beginning of his career he, in collaboration with Dynkin, worked on nonlinear stochastic control theory, making advances in the study of convex, nonlinear partial equations of 2nd order, which were examined with stochastic methods. This led to the Evans-Krylov theory, for which he received with Lawrence C. Evans in 2004 the Leroy P. Steele Prize of the American Mathematical Society. They proved the second order differentiability of the solutions of convex, completely nonlinear, second order elliptical partial differential equations and thus the existence of "classical solutions". He was in 1978 at Helsinki and in 1986 at Berkeley an Invited Speaker for the ICM. He received the Humboldt Research Award in 2001. In 1993 he was elected a member of the American Academy of Arts and Sciences. He should not be confused with the mathematician Nikolay M. Krylov.

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