An obstacle problem for Tug-of-War games

Juan J. Manfredi; Julio D. Rossi; Stephanie J. Somersille

doi:10.3934/cpaa.2015.14.217

Article Contents

2015, Volume 14, Issue 1: 217-228. Doi: 10.3934/cpaa.2015.14.217

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An obstacle problem for Tug-of-War games

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
2.
Departamento de Análisis Matemático, Universidad de Alicante, Ap 99, 03080, Alicante
3.
Department of Mathematics, Dartmouth College, Hanover, NH 03755

Received: February 28, 2014

Revised: March 31, 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J60, 91A05, 49L25, 35J25.

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