A mixed problem for the infinity Laplacian via Tug-of-War games

In this paper we prove that a function uC} overlineΩ is the continuous value of the Tug-of-War game described in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear) if and only if it is the unique viscosity solution to the infinity Laplacian with mixed boundary conditions equation presented. By usi...

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Autor principal: Rossi, Julio Daniel
Publicado: 2009
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v34_n3_p307_Charro
http://hdl.handle.net/20.500.12110/paper_09442669_v34_n3_p307_Charro
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_09442669_v34_n3_p307_Charro2023-06-08T15:53:46Z A mixed problem for the infinity Laplacian via Tug-of-War games Rossi, Julio Daniel In this paper we prove that a function uC} overlineΩ is the continuous value of the Tug-of-War game described in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear) if and only if it is the unique viscosity solution to the infinity Laplacian with mixed boundary conditions equation presented. By using the results in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear), it follows that this viscous PDE problem has a unique solution, which is the unique absolutely minimizing Lipschitz extension to the whole Ω (in the sense of Aronsson (Ark. Mat. 6:551-561, 1967) and Y. Peres et al. (J. Am. Math. Soc., 2008, to appear)) of the Lipschitz boundary data F:ΓD R . © 2008 Springer-Verlag. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v34_n3_p307_Charro http://hdl.handle.net/20.500.12110/paper_09442669_v34_n3_p307_Charro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper we prove that a function uC} overlineΩ is the continuous value of the Tug-of-War game described in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear) if and only if it is the unique viscosity solution to the infinity Laplacian with mixed boundary conditions equation presented. By using the results in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear), it follows that this viscous PDE problem has a unique solution, which is the unique absolutely minimizing Lipschitz extension to the whole Ω (in the sense of Aronsson (Ark. Mat. 6:551-561, 1967) and Y. Peres et al. (J. Am. Math. Soc., 2008, to appear)) of the Lipschitz boundary data F:ΓD R . © 2008 Springer-Verlag.
author Rossi, Julio Daniel
spellingShingle Rossi, Julio Daniel
A mixed problem for the infinity Laplacian via Tug-of-War games
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title A mixed problem for the infinity Laplacian via Tug-of-War games
title_short A mixed problem for the infinity Laplacian via Tug-of-War games
title_full A mixed problem for the infinity Laplacian via Tug-of-War games
title_fullStr A mixed problem for the infinity Laplacian via Tug-of-War games
title_full_unstemmed A mixed problem for the infinity Laplacian via Tug-of-War games
title_sort mixed problem for the infinity laplacian via tug-of-war games
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v34_n3_p307_Charro
http://hdl.handle.net/20.500.12110/paper_09442669_v34_n3_p307_Charro
work_keys_str_mv AT rossijuliodaniel amixedproblemfortheinfinitylaplacianviatugofwargames
AT rossijuliodaniel mixedproblemfortheinfinitylaplacianviatugofwargames
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