A limiting free boundary problem with gradient constraint and Tug-of-War games

In this manuscript we deal with regularity issues and the asymptotic behaviour (as p→ ∞) of solutions for elliptic free boundary problems of p- Laplacian type (2 ≤ p< ∞): -Δpu(x)+λ0(x)χ{u>0}(x)=0inΩ⊂RN,with a prescribed Dirichlet boundary data, where λ> 0 is a bounded function and Ω is a re...

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Detalles Bibliográficos
Autores principales:	Blanc, P., da Silva, J.V., Rossi, J.D.
Formato:	JOUR
Materias:	Existence/uniqueness of solutions Free boundary problems Lipschitz regularity estimates Tug-of-War games ∞-Laplace operator
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Blanc
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_03733114_v_n_p_Blanc2023-10-03T15:30:21Z A limiting free boundary problem with gradient constraint and Tug-of-War games Blanc, P. da Silva, J.V. Rossi, J.D. Existence/uniqueness of solutions Free boundary problems Lipschitz regularity estimates Tug-of-War games ∞-Laplace operator In this manuscript we deal with regularity issues and the asymptotic behaviour (as p→ ∞) of solutions for elliptic free boundary problems of p- Laplacian type (2 ≤ p< ∞): -Δpu(x)+λ0(x)χ{u>0}(x)=0inΩ⊂RN,with a prescribed Dirichlet boundary data, where λ> 0 is a bounded function and Ω is a regular domain. First, we prove the convergence as p→ ∞ of any family of solutions (up)p≥2, as well as we obtain the corresponding limit operator (in non-divergence form) ruling the limit equation, {max{-Δ∞u∞,-\|∇u∞\|+χ{u∞>0}}=0inΩ∩{u∞≥0}u∞=Fon∂Ω.Next, we obtain uniqueness for solutions to this limit problem. Finally, we show that any solution to the limit operator is a limit of value functions for a specific Tug-of-War game. © 2019, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Blanc
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Existence/uniqueness of solutions Free boundary problems Lipschitz regularity estimates Tug-of-War games ∞-Laplace operator
spellingShingle	Existence/uniqueness of solutions Free boundary problems Lipschitz regularity estimates Tug-of-War games ∞-Laplace operator Blanc, P. da Silva, J.V. Rossi, J.D. A limiting free boundary problem with gradient constraint and Tug-of-War games
topic_facet	Existence/uniqueness of solutions Free boundary problems Lipschitz regularity estimates Tug-of-War games ∞-Laplace operator
description	In this manuscript we deal with regularity issues and the asymptotic behaviour (as p→ ∞) of solutions for elliptic free boundary problems of p- Laplacian type (2 ≤ p< ∞): -Δpu(x)+λ0(x)χ{u>0}(x)=0inΩ⊂RN,with a prescribed Dirichlet boundary data, where λ> 0 is a bounded function and Ω is a regular domain. First, we prove the convergence as p→ ∞ of any family of solutions (up)p≥2, as well as we obtain the corresponding limit operator (in non-divergence form) ruling the limit equation, {max{-Δ∞u∞,-\|∇u∞\|+χ{u∞>0}}=0inΩ∩{u∞≥0}u∞=Fon∂Ω.Next, we obtain uniqueness for solutions to this limit problem. Finally, we show that any solution to the limit operator is a limit of value functions for a specific Tug-of-War game. © 2019, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.
format	JOUR
author	Blanc, P. da Silva, J.V. Rossi, J.D.
author_facet	Blanc, P. da Silva, J.V. Rossi, J.D.
author_sort	Blanc, P.
title	A limiting free boundary problem with gradient constraint and Tug-of-War games
title_short	A limiting free boundary problem with gradient constraint and Tug-of-War games
title_full	A limiting free boundary problem with gradient constraint and Tug-of-War games
title_fullStr	A limiting free boundary problem with gradient constraint and Tug-of-War games
title_full_unstemmed	A limiting free boundary problem with gradient constraint and Tug-of-War games
title_sort	limiting free boundary problem with gradient constraint and tug-of-war games
url	http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Blanc
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A limiting free boundary problem with gradient constraint and Tug-of-War games

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