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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.06357 |
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| _version_ | 1866911785517318144 |
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| author | Allen, Mark Garcia, Mariana Smit Vega |
| author_facet | Allen, Mark Garcia, Mariana Smit Vega |
| contents | In this paper, we study almost minimizers to a fractional Alt-Caffarelli-Friedman type functional. Our main results concern the optimal $C^{0,s}$ regularity of almost minimizers as well as the structure of the free boundary. We first prove that the two free boundaries $F^+(u)=\partial\{u(\cdot,0)>0\}$ and $F^-(u)=\partial\{u(\cdot,0)<0\}$ cannot touch, that is, $F^+(u)\cap F^-(u)=\emptyset$. Lastly, we prove a flatness implies $C^{1,γ}$ result for the free boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-phase almost minimizers for a fractional free boundary problem Allen, Mark Garcia, Mariana Smit Vega Analysis of PDEs In this paper, we study almost minimizers to a fractional Alt-Caffarelli-Friedman type functional. Our main results concern the optimal $C^{0,s}$ regularity of almost minimizers as well as the structure of the free boundary. We first prove that the two free boundaries $F^+(u)=\partial\{u(\cdot,0)>0\}$ and $F^-(u)=\partial\{u(\cdot,0)<0\}$ cannot touch, that is, $F^+(u)\cap F^-(u)=\emptyset$. Lastly, we prove a flatness implies $C^{1,γ}$ result for the free boundary. |
| title | Two-phase almost minimizers for a fractional free boundary problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.06357 |