AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS RELATED TO TUG-OF-WAR GAMES

被引：65

作者：

Manfredi, Juan J. ^{[1
]}

Parviainen, Mikko ^{[2
]}

Rossi, Julio D. ^{[3
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Aalto Univ, Sch Sci & Technol, FI-00076 Helsinki, Finland

[3] Univ Alicante, Dept Anal Matemat, E-03080 Alicante, Spain

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 05期

基金：

美国国家科学基金会;

关键词：

Dirichlet boundary conditions; dynamic programming principle; parabolic p-Laplacian; parabolic mean value property; stochastic games; tug-of-war games with limited number of rounds; viscosity solutions; MINIMIZING LIPSCHITZ EXTENSIONS; INFINITY LAPLACIAN; VISCOSITY SOLUTIONS; CURVATURE;

D O I：

10.1137/100782073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize solutions to the homogeneous parabolic p-Laplace equation u(t) - vertical bar del u|(2-p)Delta(p)u = (p - 2)Delta(infinity)u + Delta u in terms of an asymptotic mean value property. The results are connected with the analysis of tug-of-war games with noise in which the number of rounds is bounded. The value functions for these games approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero.

引用

页码：2058 / 2081

页数：24