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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.18327 |
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| _version_ | 1866916450596290560 |
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| author | Hara, Takanobu |
| author_facet | Hara, Takanobu |
| contents | This is a progress report on study of uniformly elliptic Poisson-type equations on domains with capacity density conditions (CDC domains). We give a brief summary of known facts of CDC domains, including Hardy's inequality, and review a previous work of existence of globally Hölder continuous solutions. Additionally, we apply the result to homogenization problems of $ε$-periodic coefficients and present a convergence rate estimate of $L^{\infty}$ norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of Hölder Continuous Solutions and Homogenization Results Hara, Takanobu Analysis of PDEs This is a progress report on study of uniformly elliptic Poisson-type equations on domains with capacity density conditions (CDC domains). We give a brief summary of known facts of CDC domains, including Hardy's inequality, and review a previous work of existence of globally Hölder continuous solutions. Additionally, we apply the result to homogenization problems of $ε$-periodic coefficients and present a convergence rate estimate of $L^{\infty}$ norms. |
| title | Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of Hölder Continuous Solutions and Homogenization Results |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.18327 |