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

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.