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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Detalles Bibliográficos
Autores principales: Manfredi, J.J., Parviainenf, M., Rossi, J.D.
Formato: JOUR
Materias:
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
Mean values
P-Laplacian
Stochastic game
Asymptotic analysis
Boundary conditions
Laplace equation
Laplace transforms
Nonlinear equations
Stochastic systems
Viscosity
Dynamic programming
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361410_v42_n5_p2058_Manfredi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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.

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