AN OBSTACLE PROBLEM FOR TUG-OF-WAR GAMES

被引：9
|
作者：
Manfredi, Juan J. [1 ]
Rossi, Julio D. [2 ,3 ]
Somersille, Stephanie J. [4 ]
机构：
[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
[2] Univ Alicante, Dept Anal Matemat, E-03080 Alicante, Spain
[3] Univ Buenos Aires, FCEyN, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina
[4] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 01期
基金：
美国国家科学基金会;
关键词：
Obstacle Problem; Tug-of-War games; infinity laplacian; MEAN-VALUE CHARACTERIZATION;
D O I：
10.3934/cpaa.2015.14.217
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the obstacle problem for the infinity Laplace equation. Given a Lipschitz boundary function and a Lipschitz obstacle we prove the existence and uniqueness of a super infinity-harmonic function constrained to lie above the obstacle which is infinity harmonic where it lies strictly above the obstacle. Moreover, we show that this function is the limit of value functions of a game we call obstacle tug-of-war.
引用
收藏
页码：217 / 228
页数：12
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