Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions

2025/10/31 by Han, Yuxi, Tu, Son
#35B10 #35B27 #35B40 #35F21 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.27099

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 O(ε) 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.

Citations

• On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
• Quantitative homogenization of convex Hamilton-Jacobi equations with Neumann type boundary conditions
• Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems
• Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
• Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications
• Rate of Convergence in Periodic Homogenization for Convex Hamilton-Jacobi Equations with Multiscales
• On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations
• Optimal convergence rate for homogenization of convex Hamilton-Jacobi equations in the periodic spatial-temporal environment
• Optimal convergence rate for periodic homogenization of convex Hamilton-Jacobi equations
• Effective fronts of polytope shapes
• Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting

Related

• Quantitative homogenization of convex Hamilton-Jacobi equations with Neumann type boundary conditions
• Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications
• Optimal convergence rate for periodic homogenization of convex Hamilton-Jacobi equations
• Rate of Convergence in Periodic Homogenization for Convex Hamilton-Jacobi Equations with Multiscales
• Optimal convergence rate for homogenization of convex Hamilton-Jacobi equations in the periodic spatial-temporal environment