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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
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
Palabras clave:Infinity Laplacian; Tug-of-war games; Viscosity solutions
Año:2013
Volumen:12
Número:5
Página de inicio:1959
Página de fin:1983
DOI: http://dx.doi.org/10.3934/cpaa.2013.12.1959
Título revista:Communications on Pure and Applied Analysis
Título revista abreviado:Commun. Pure Appl. Anal.
ISSN:15340392
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