Abstract:
In this paper we look for PDEs that arise as limits of values of tug-of-war games when the possible movements of the game are taken in a family of sets that are not necessarily Euclidean balls. In this way we find existence of cviscosity solutions to the Dirichlet problem for an equation of the form -(D2v · Jx(Dv); Jx(Dv))(x) = 0, that is, an infinity Laplacian with spatial dependence. Here Jx(Dv(x)) is a vector that depends on the spatial location and the gradient of the solution.
Registro:
Documento: |
Artículo
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Título: | Tug-of-war games and the infinity laplacian with spatial dependence |
Autor: | Gómez, I.; Rossi, J.D. |
Filiación: | Instituto de Matemática Aplicada del Litoral (IMAL), CONICET-UNL Departamento de Matemática, Facultad de Ingeniería Química, UNL Güemes 3450, S3000GLN Santa Fe, Argentina Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080, Alicante, Spain Departamento de Matemática, FCEyN, UBA Ciudad Universitaria Pab.1, 1428 Buenos Aires, Argentina
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Palabras clave: | Infinity Laplacian; Tug-of-war games; Viscosity solutions |
Año: | 2013
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Volumen: | 12
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Número: | 5
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Página de inicio: | 1959
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Página de fin: | 1983
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DOI: |
http://dx.doi.org/10.3934/cpaa.2013.12.1959 |
Título revista: | Communications on Pure and Applied Analysis
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Título revista abreviado: | Commun. Pure Appl. Anal.
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ISSN: | 15340392
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v12_n5_p1959_Gomez |
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Citas:
---------- APA ----------
Gómez, I. & Rossi, J.D.
(2013)
. Tug-of-war games and the infinity laplacian with spatial dependence. Communications on Pure and Applied Analysis, 12(5), 1959-1983.
http://dx.doi.org/10.3934/cpaa.2013.12.1959---------- CHICAGO ----------
Gómez, I., Rossi, J.D.
"Tug-of-war games and the infinity laplacian with spatial dependence"
. Communications on Pure and Applied Analysis 12, no. 5
(2013) : 1959-1983.
http://dx.doi.org/10.3934/cpaa.2013.12.1959---------- MLA ----------
Gómez, I., Rossi, J.D.
"Tug-of-war games and the infinity laplacian with spatial dependence"
. Communications on Pure and Applied Analysis, vol. 12, no. 5, 2013, pp. 1959-1983.
http://dx.doi.org/10.3934/cpaa.2013.12.1959---------- VANCOUVER ----------
Gómez, I., Rossi, J.D. Tug-of-war games and the infinity laplacian with spatial dependence. Commun. Pure Appl. Anal. 2013;12(5):1959-1983.
http://dx.doi.org/10.3934/cpaa.2013.12.1959