Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
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| Format: | Preprint |
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2024
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| _version_ | 1866917875223101440 |
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| 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 |
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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 |