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.
Keywords
Hamilton–Jacobi equation; stochastic homogenization; stationary ergodic random environment; differential games: viscosity solution;
Reference
Andrea Davini, Raimundo Saona, and Bruno Ziliotto, “Stochastic homogenization of HJ equations: A differential game approach”, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire Open Archive, vol. 43, n. 4, 2026, pp. 883–925.
Published in
Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire Open Archive, vol. 43, n. 4, 2026, pp. 883–925