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

Fuente: arXiv
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Main Authors: Hu, Bingyang, Tu, Son N. T., Zhang, Jianlu
Format: Preprint
Published: 2024
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_version_ 1866917875223101440
author Hu, Bingyang
Tu, Son N. T.
Zhang, Jianlu
author_facet Hu, Bingyang
Tu, Son N. T.
Zhang, Jianlu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_11516
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
Hu, Bingyang
Tu, Son N. T.
Zhang, Jianlu
Analysis of PDEs
35B10, 35B27, 35B40, 35F21, 49L25
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.
title Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
topic Analysis of PDEs
35B10, 35B27, 35B40, 35F21, 49L25
url https://arxiv.org/abs/2405.11516