Nicolai V. Krylov

Nikolai Vladimirovich Krylov (Russian Николай Владимирович Крылов, cited in English as Nicolai V. Krylov, born June 5, 1941 in Sudogda, Vladimir Oblast ) is a Russian mathematician who deals with partial differential equations, specifically stochastic partial differential equations and diffusion processes.

Krylov studied at the Moscow State University, where he received his doctorate in 1966 at EB Dynkin ( candidate titles) and his habilitation in 1973 (Russian doctorate degrees). He taught from 1966 to 1990 at the Moscow State University and since 1990 professor at the University of Minnesota.

Initially ( in 1963 ) he worked, inspired by Dynkin, via nonlinear stochastic control theory, what convex to the study, nonlinear partial equations of 2nd order leads ( Bellman equations) that have been studied with stochastic methods. This led him to the Evans - Krylov theory, for which he and Lawrence C. Evans received the Leroy P. Steele Prize of the American Mathematical Society 2004 ( simultaneously and independently by two developed ). They proved it convex twice differentiable ( Hölder continuity of the second derivatives ) of the solutions completely nonlinear, uniformly elliptic partial differential equations and thus the existence of "classical solutions " ( set of Evans - Krylov ).

He was in 1978 in Helsinki and 1986 in Berkeley Invited Speaker on the ICM. In 2001 he received the Humboldt Research Award. He is a member of the American Academy of Arts and Sciences (1993).

He should not be confused with the mathematician Nikolai Krylov Mitrofanovich.

Writings

• Controlled diffusion processes, Springer 1980
• Introduction to the theory of diffusion processes, AMS 1995
• Nonlinear elliptic and parabolic equations of the second order, Dordrecht, Reidel 1987
• Lectures on elliptic and parabolic equations in Holder Spaces, AMS 1996
• Introduction to the theory of random processes, AMS 2002