Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications

TL;DR

This paper investigates the homogenization of state-constraint Hamilton-Jacobi equations on perforated domains, achieving optimal convergence rates and exploring dilute and defective domain scenarios.

Contribution

It introduces new homogenization results for Hamilton-Jacobi equations on complex perforated domains, including dilute and defective cases, with optimal convergence rates.

Findings

Established optimal convergence rates for homogenization.

Analyzed homogenization in dilute hole configurations.

Studied effects of domain defects with missing holes.

Abstract

We study the periodic homogenization problem of state-constraint Hamilton--Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the holes' diameter is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.