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

2024/05/19 by Bingyang Hu, Hu, Bingyang, Son N. T. Tu +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2405.11516

Abstract

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.

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• Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
• Quantitative homogenization of first-order ODEs

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