Nikolai Vladimirovich Krylov

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Nicolai V. Krylov ( Russian Николай Владимирович Крылов , quoted in English as Nicolai V. Krylov * 5. June 1941 in Sudogda , Vladimir Oblast ) is a Russian mathematician who with partial differential equations busy, especially stochastic partial differential equations and diffusion processes .

Krylov studied at Lomonosov University , where he received his doctorate from EB Dynkin in 1966 (candidate title) and completed his habilitation in 1973 (Russian doctoral degree). He taught at Lomonosov University from 1966 to 1990 and has been a professor at the University of Minnesota since 1990 .

At the beginning (from 1963), stimulated by Dynkin, he worked on nonlinear stochastic control theory , which led to the study of convex, nonlinear partial equations of the 2nd order ( Bellman equations), which were investigated 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 in 2004 (developed simultaneously and independently of both). They proved the twofold differentiability ( Hölder continuity of the second derivatives) of the solutions of convex, completely nonlinear, uniformly elliptical partial differential equations and thus the existence of “classical solutions” (Evans-Krylov theorem).

He was invited speaker at the ICM in Helsinki in 1978 and in Berkeley in 1986 . 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 Mitrofanovich Krylov .

Fonts

  • 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

Web links

Individual evidence

  1. ↑ the non-linearity is a convex function
  2. ↑ Krylov "Boundedly inhomogeneous elliptic and parabolic equations", Istvestija Akademia Nauka SSR, Series Mathematics, Vol. 46, 1982, p. 487.
personal data
SURNAME Krylov, Nikolai Vladimirovich
ALTERNATIVE NAMES Krylov, Nicolai V. (English); Крылов, Николай Владимирович (Russian)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH June 5, 1941
PLACE OF BIRTH Sudogda , Vladimir Oblast