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
Publicado: 2019
Materias:
Existence/uniqueness of solutions
Free boundary problems
Lipschitz regularity estimates
Tug-of-War games
∞-Laplace operator
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v_n_p_Blanc
http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Blanc
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03733114_v_n_p_Blanc
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spelling paper:paper_03733114_v_n_p_Blanc2023-06-08T15:37:57Z A limiting free boundary problem with gradient constraint and Tug-of-War games 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. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v_n_p_Blanc 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
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.
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
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v_n_p_Blanc
http://hdl.handle.net/20.500.12110/paper_03733114_v_n_p_Blanc
_version_ 1768546025053618176

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