Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates

Bingyang Hu; Jianlu Zhang; Son N.T. Tu

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arxiv 2405.11516 v4 pith:5GPLR3SC submitted 2024-05-19 math.AP

Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates

Bingyang Hu , Son N.T. Tu , Jianlu Zhang This is my paper

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keywords quasi-periodicrateconvergencehomogenizationapplicationequationsergodicfunctions

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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.

Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates

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