Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908622450065408 |
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| author | Han, Yuxi Tu, Son |
| author_facet | Han, Yuxi Tu, Son |
| contents | We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function associated with the running cost, we establish the optimal convergence rate $\mathcal{O}(\varepsilon)$ for homogenization. A key aspect of our approach is the treatment of the singularity that arises when the optimal path does not fully utilize the available time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions Han, Yuxi Tu, Son Analysis of PDEs 35B10, 35B27, 35B40, 35F21, 49L25 We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function associated with the running cost, we establish the optimal convergence rate $\mathcal{O}(\varepsilon)$ for homogenization. A key aspect of our approach is the treatment of the singularity that arises when the optimal path does not fully utilize the available time. |
| title | Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions |
| topic | Analysis of PDEs 35B10, 35B27, 35B40, 35F21, 49L25 |
| url | https://arxiv.org/abs/2510.27099 |