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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.09378 |
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| _version_ | 1866913543365853184 |
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| author | Kim, Sunghoon Lee, Ki-Ahm Lee, Se-Chan Yoo, Minha |
| author_facet | Kim, Sunghoon Lee, Ki-Ahm Lee, Se-Chan Yoo, Minha |
| contents | We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly oscillating corrector, which captures the singular behavior of solutions near periodically distributed holes of critical size. We then prove the uniqueness of a critical value that encodes the coupled effects of oscillations in both the coefficients and the obstacles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homogenization of an obstacle problem with highly oscillating coefficients and obstacles Kim, Sunghoon Lee, Ki-Ahm Lee, Se-Chan Yoo, Minha Analysis of PDEs 35B27, 35D40, 35R35 We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly oscillating corrector, which captures the singular behavior of solutions near periodically distributed holes of critical size. We then prove the uniqueness of a critical value that encodes the coupled effects of oscillations in both the coefficients and the obstacles. |
| title | Homogenization of an obstacle problem with highly oscillating coefficients and obstacles |
| topic | Analysis of PDEs 35B27, 35D40, 35R35 |
| url | https://arxiv.org/abs/2410.09378 |