Regularity of two-phase free boundary minimizers in periodic media
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916752403726336 |
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| author | Abedin, Farhan Feldman, William M |
| author_facet | Abedin, Farhan Feldman, William M |
| contents | We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flatness for non-degenerate minimizers, which is a key ingredient in the proof of the Lipschitz estimate. As a consequence, we obtain a Liouville property for entire non-degenerate minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity of two-phase free boundary minimizers in periodic media Abedin, Farhan Feldman, William M Analysis of PDEs 5R35, 35B27, 35B65, 49Q05 We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flatness for non-degenerate minimizers, which is a key ingredient in the proof of the Lipschitz estimate. As a consequence, we obtain a Liouville property for entire non-degenerate minimizers. |
| title | Regularity of two-phase free boundary minimizers in periodic media |
| topic | Analysis of PDEs 5R35, 35B27, 35B65, 49Q05 |
| url | https://arxiv.org/abs/2505.16757 |