基于微分博弈方法的 Hamilton-Jacobi 方程随机均质化
偏微分方程分析
2025-10-30 v2
摘要
We prove stochastic homogenization for a class of non-convex and non-coercive 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.
引用
@article{arxiv.2406.18404,
title = {Stochastic Homogenization of HJ Equations: a Differential Game Approach},
author = {Andrea Davini and Raimundo Saona and Bruno Ziliotto},
journal= {arXiv preprint arXiv:2406.18404},
year = {2025}
}