An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games
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 thes...
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v42_n5_p2058_Manfredi http://hdl.handle.net/20.500.12110/paper_00361410_v42_n5_p2058_Manfredi |
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paper:paper_00361410_v42_n5_p2058_Manfredi2023-06-08T15:01:55Z An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games Rossi, Julio Daniel 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 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v42_n5_p2058_Manfredi http://hdl.handle.net/20.500.12110/paper_00361410_v42_n5_p2058_Manfredi |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Rossi, Julio Daniel An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| topic_facet |
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 |
| description |
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. |
| author |
Rossi, Julio Daniel |
| author_facet |
Rossi, Julio Daniel |
| author_sort |
Rossi, Julio Daniel |
| title |
An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| title_short |
An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| title_full |
An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| title_fullStr |
An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| title_full_unstemmed |
An asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| title_sort |
asymptotic mean value chara cterization for a class of nonlinear parabolic equations related to tug-of-war games |
| publishDate |
2010 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v42_n5_p2058_Manfredi http://hdl.handle.net/20.500.12110/paper_00361410_v42_n5_p2058_Manfredi |
| work_keys_str_mv |
AT rossijuliodaniel anasymptoticmeanvaluecharacterizationforaclassofnonlinearparabolicequationsrelatedtotugofwargames AT rossijuliodaniel asymptoticmeanvaluecharacterizationforaclassofnonlinearparabolicequationsrelatedtotugofwargames |
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1768546151137542144 |