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.
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页码：2058 / 2081
页数：24
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