Lars Valter Hörmander was a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". Hörmander was awarded the Fields Medal in 1962 and the Wolf Prize in 1988. In 2006 he was awarded the Steele Prize for Mathematical Exposition for his four-volume textbook Analysis of Linear Partial Differential Operators, which is considered a foundational work on the subject.
The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function. Its solution is the value function of the optimal control problem which, once known, can be used to obtain the optimal control by taking the maximizer of the Hamiltonian involved in the HJB equation.
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Pierre-Louis Lions is a French mathematician. He is known for a number of contributions to the fields of partial differential equations and the calculus of variations. He was a recipient of the 1994 Fields Medal and the 1991 Prize of the Philip Morris tobacco and cigarette company.
Oskar Perron was a German mathematician.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example first order equations arising in dynamic programming, differential games or front evolution problems, as well as second-order equations such as the ones arising in stochastic optimal control or stochastic differential games.
In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods.
Henry P. McKean, Jr. is an American mathematician at the Courant Institute in New York University. He works in various areas of analysis. He obtained his PhD in 1955 from Princeton University under William Feller.
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 (1993). He should not be confused with the mathematician Nikolay M. Krylov.
Michael Grain Crandall is an American mathematician, specializing in differential equations.
J. (Jean) François Treves is an American mathematician, specializing in partial differential equations.
Ronald J. DiPerna was an American mathematician, who worked on nonlinear partial differential equations.
Edward Norman Dancer FAA is an Australian mathematician, specializing in nonlinear analysis.
Victor Lenard Shapiro was an American mathematician, specializing in trigonometric series and differential equations. He is known for his two theorems on the uniqueness of multiple Fourier series.
Hitoshi Ishii, a Japanese mathematician, who is specialized in partial differential equations.
Robert Ronald Jensen is an American mathematician, specializing in nonlinear partial differential equations with applications to physics, engineering, game theory, and finance.
Panagiotis E. Souganidis is an American mathematician, specializing in partial differential equations.
Joel Spruck is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971.
Klaus Schmitt is an American mathematician doing research in nonlinear differential equations, and nonlinear analysis.
