# Asymptotic mean value formulas for parabolic nonlinear equations

@article{Blanc2022AsymptoticMV, title={Asymptotic mean value formulas for parabolic nonlinear equations}, author={Pablo Blanc and Fernando Charro and Juan J. Manfredi and Julio D. Rossi}, journal={Revista de la Uni{\'o}n Matem{\'a}tica Argentina}, year={2022} }

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.

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…

On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge–Ampère equations

- Mathematics
- 2011

Subharmonic functions in sub-Riemannian settings

- Mathematics
- 2010

In this note we present mean value characterizations of subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a…