Tug-of-war games and PDEs

被引：19

作者：

Rossi, Julio D. ^{[1
]}

机构：

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2011年 / 141卷

关键词：

MINIMIZING LIPSCHITZ EXTENSIONS; INFINITY-EIGENVALUE PROBLEM; MASS-TRANSFER PROBLEM; DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; HARMONIC FUNCTIONS; P-LAPLACIAN; UNIQUENESS;

D O I：

10.1017/S0308210510000041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We review some recent results concerning tug-of-war games and their relation to some well-known partial differential equations (PDEs). In particular, we will show that solutions to certain PDEs can be obtained as limits of values of tug-of-war games when the parameter that controls the length of the possible movements goes to zero. Since the equations being studied are nonlinear and are not in divergence form, we will make extensive use of the concept of viscosity solutions.

引用

页码：319 / 369

页数：51

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