Games for Pucci's maximal operators

TL;DR

This paper introduces a game-theoretic approach where the value functions approximate solutions to Pucci's maximal operators, linking game theory with nonlinear PDEs.

Contribution

The paper presents a novel game model whose value functions converge to solutions of Pucci's maximal operators, bridging game theory and nonlinear PDE analysis.

Findings

Value functions converge uniformly to PDE solutions

Game model provides a new approach to nonlinear PDEs

Links between game theory and Pucci operators established

Abstract

In this paper we introduce a game whose value functions converge (as a parameter that measures the size of the steps goes to zero) uniformly to solutions to the second order Pucci maximal operators.