Solutions of nonlinear PDEs in the sense of averages

被引：46

作者：

Kawohl, Bernd ^{[1
]}

Manfredi, Juan ^{[2
]}

Parviainen, Mikko ^{[3
]}

机构：

[1] Univ Cologne, Inst Math, D-50923 Cologne, Germany

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

[3] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla 40014, Finland

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2012年 / 97卷 / 02期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

1-harmonic; Asymptotic expansion; Dynamic programming principle; Mean value theorem; p-harmonic; Stochastic games; Two-player zero-sum games; Viscosity solutions; TUG-OF-WAR; PARTIAL-DIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS; INFINITY LAPLACIAN; P-LAPLACIAN; MEAN-CURVATURE; EXTENSIONS; MOTION;

D O I：

10.1016/j.matpur.2011.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize p-harmonic functions including p = 1 and p = infinity by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all p's. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 < p < infinity. (C) 2011 Elsevier Masson SAS. All rights reserved.

引用

页码：173 / 188

页数：16

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