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Abstract:

We characterize solutions to the homogeneous parabolic p-Laplace equation ut = |∇u|2-pΔpu = (p - 2)Δ∞u + Δu in terms of an asymptotic mean value property. The results are connected with the analysis of tug-of-war games with noise in which the number of rounds is bounded. The value functions for these games approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Registro:

Documento: Artículo
Título:An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games
Autor:Manfredi, J.J.; Parviainenf, M.; Rossi, J.D.
Filiación:Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States
Aalto University, School of Science and Technology, P.O. Box 11000, FI-00076 Aalto, Helsinki, Finland
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain
Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina
Palabras clave:Dirichlet boundary conditions; Dynamic programming principle; Parabolic mean value property; Parabolic p-laplacian; Stochastic games; Tug-of-war games with limited number of rounds; Viscosity solutions; Dirichlet boundary condition; Dynamic programming principle; Mean values; P-Laplacian; Stochastic game; Tug-of-war games with limited number of rounds; Viscosity solutions; Asymptotic analysis; Boundary conditions; Laplace equation; Laplace transforms; Nonlinear equations; Stochastic systems; Viscosity; Dynamic programming
Año:2010
Volumen:42
Número:5
Página de inicio:2058
Página de fin:2081
DOI: http://dx.doi.org/10.1137/100782073
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v42_n5_p2058_Manfredi

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Citas:

---------- APA ----------
Manfredi, J.J., Parviainenf, M. & Rossi, J.D. (2010) . An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games. SIAM Journal on Mathematical Analysis, 42(5), 2058-2081.
http://dx.doi.org/10.1137/100782073
---------- CHICAGO ----------
Manfredi, J.J., Parviainenf, M., Rossi, J.D. "An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games" . SIAM Journal on Mathematical Analysis 42, no. 5 (2010) : 2058-2081.
http://dx.doi.org/10.1137/100782073
---------- MLA ----------
Manfredi, J.J., Parviainenf, M., Rossi, J.D. "An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games" . SIAM Journal on Mathematical Analysis, vol. 42, no. 5, 2010, pp. 2058-2081.
http://dx.doi.org/10.1137/100782073
---------- VANCOUVER ----------
Manfredi, J.J., Parviainenf, M., Rossi, J.D. An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games. SIAM J. Math. Anal. 2010;42(5):2058-2081.
http://dx.doi.org/10.1137/100782073