Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
Bingyang Hu, Son N. T. Tu, Jianlu Zhang · arXiv (Cornell University) · 2024
In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the convergence rate of homogenization and the regularity of the effective Hamiltonian, by using a new quantitative ergodic estimate for bounded quasi-periodic functions with Diophantine frequencies. As an application, we also study the convergent rate for Birkhoff average of unbounded quasi-periodic functions.