Stochastic homogenization of HJ equations: A differential game approach
Abstract
We prove stochastic homogenization for a class of nonconvex and noncoercive first-order Hamilton–Jacobi equations in a finite-range dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the representation of solutions as value functions of differential games, we develop a game-theoretic approach to homogenization. We furthermore extend this result to a class of Lipschitz Hamiltonians that need not admit a global max-min representation. Our methods allow us to get a quantitative convergence rate for solutions with linear initial data toward the corresponding ones of the effective limit problem.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Annales de l Institut Henri Poincaré C Analyse Non Linéaire
- Volume
- 43
- Issue
- 4
- Pages
- 883–925
- Publication date
- 26 February 2026
- Language
- EN