Quantitative Homogenization of State-Constraint Hamilton–Jacobi Equations on Perforated Domains and Applications - Han, Yuxi; Jing, Wenjia; Mitake, Hiroyoshi; Tran, Hung V. (Archive for rational mechanics and analysis, 2025)
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 diameter of the holes is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.