Polynomial convergence rate for quasi-periodic homogenization of Hamilton-Jacobi equations and application to ergodic estimates

被引：0

作者：

Hu, Bingyang ^{[1
]}

Tu, Son N. T. ^{[2
]}

Zhang, Jianlu ^{[3
,4
]}

机构：

[1] Auburn Univ, Dept Math & Stat, Auburn, AL USA

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[3] Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China

[4] Chinese Acad Sci, Math Inst, Acad Math & Syst Sci, Beijing, Peoples R China

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2025年 / 50卷 / 1-2期

基金：

国家重点研发计划;

关键词：

Hamilton-Jacobi equations; homogenization; quasi-periodic function; rate of convergence; viscosity solutions; STOCHASTIC HOMOGENIZATION; VISCOSITY SOLUTIONS;

D O I：

10.1080/03605302.2024.2446459

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, 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.

引用

页码：211 / 244

页数：34