Nicolai Vladimirovich Krylov (russian: Никола́й Влади́мирович Крыло́в; born 5 June 1941) is a Russian mathematician specializing in
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s, particularly
stochastic partial differential equation
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations.
They have ...
s and
diffusion processes. Krylov studied at
Lomonosov University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
, where he in 1966 under
E. B. Dynkin attained a doctoral candidate title (similar to a PhD) and in 1973 a Russian doctoral degree (somewhat more prestigious than a PhD). 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 (starting from 1963) he, in collaboration with Dynkin, worked on nonlinear stochastic
control theory, making advances in the study of convex, nonlinear partial equations of 2nd order (''i.e.''
Bellman
Bellman may refer to:
* Town crier, an officer of the court who makes public pronouncements
* Bellhop, a hotel porter
* Bellman (surname)
* Bellman (diving), a standby diver and diver's attendant
* Bellman hangar, a prefabricated, portable aircraf ...
equations), which were examined with stochastic methods. This led to the Evans-Krylov theory, for which he received with
Lawrence C. Evans
Lawrence Craig Evans (born November 1, 1949) is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
His research is in the field of nonlinear partial differential equations, primarily elliptic equa ...
in 2004 the
Leroy P. Steele Prize of the
American Mathematical Society (for work done simultaneously and independently by both Krylov and Evans). They proved the second order differentiability (
Hölder continuity of the second derivative) of the solutions of convex, completely nonlinear, second order elliptical partial differential equations and thus the existence of "classical solutions" (Theorem of Evans-Krylov). He was in 1978 at
Helsinki and in 1986 at
Berkeley
Berkeley most often refers to:
*Berkeley, California, a city in the United States
**University of California, Berkeley, a public university in Berkeley, California
* George Berkeley (1685–1753), Anglo-Irish philosopher
Berkeley may also refer ...
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 (1993). He should not be confused with the mathematician
Nikolay M. Krylov.
Works
*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 Hölder Spaces, AMS 1996
*Introduction to the theory of random processes, AMS 2002
*Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, AMS 2008
References
External links
Homepage*
{{DEFAULTSORT:Krylov, Nicolai Vladimirovich
Soviet mathematicians
1941 births
Living people
Mathematical analysts
21st-century Russian mathematicians
20th-century Russian mathematicians
Fellows of the American Academy of Arts and Sciences