An obstacle problem for tug-of-war games
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 t...
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2015
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v14_n1_p217_Manfredi http://hdl.handle.net/20.500.12110/paper_15340392_v14_n1_p217_Manfredi |
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| Sumario: | 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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