Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
Analysis of PDEs
2025-11-03 v1
Abstract
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function associated with the running cost, we establish the optimal convergence rate for homogenization. A key aspect of our approach is the treatment of the singularity that arises when the optimal path does not fully utilize the available time.
Keywords
Cite
@article{arxiv.2510.27099,
title = {Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions},
author = {Yuxi Han and Son Tu},
journal= {arXiv preprint arXiv:2510.27099},
year = {2025}
}