Asymptotic mean value formulas for parabolic nonlinear equations
@inproceedings{Blanc2021AsymptoticMV, title={Asymptotic mean value formulas for parabolic nonlinear equations}, author={Pablo Blanc and Fernando Charro and Juan J. Manfredi and Julio D. Rossi}, year={2021} }
In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge-Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of Dynamic Programming Principles for certain two-player, zero-sum games.
References
SHOWING 1-10 OF 48 REFERENCES
User’s guide to viscosity solutions of second order partial differential equations
- Mathematics
- 1992
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence…
An Asymptotic Mean Value Characterization for a Class of Nonlinear Parabolic Equations Related to Tug-of-War Games
- MathematicsSIAM J. Math. Anal.
- 2010
It is shown that the value functions for tug-of-war games with noise approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero.
A mean value formula for the variational p-Laplacian
- Mathematics
- 2020
We prove a new asymptotic mean value formula for the $p$-Laplace operator, $$ \Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), $$ valid in the viscosity sense. In the plane, and for a certain range…
The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
- Mathematics
- 1985
On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂Ω
On the Mean Value Property for the p-Laplace equation in the plane
- Mathematics
- 2014
We study the p-Laplace equation in the plane and prove that the mean value property holds directly for the solutions themselves. This removes the need to interpret the formula in the viscosity sense…
A mean value theorem for the heat equation
- Mathematics
- 1966
The Gauss mean value theorem and its converse, due to Koebe, characterize solutions of Laplace's equation [2]. In view of the strong analogy between Laplace's equation and the heat equation it seems…