Optimal regularity up to the boundary for Plateau-quasi-minimizers
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912489279586304 |
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| author | Machefert, Eve |
| author_facet | Machefert, Eve |
| contents | We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with Ahlfors regular boundaries. This requires to investigate the Ahlfors regularity and also the uniform rectifiability of those sets, up to the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal regularity up to the boundary for Plateau-quasi-minimizers Machefert, Eve Optimization and Control Analysis of PDEs We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with Ahlfors regular boundaries. This requires to investigate the Ahlfors regularity and also the uniform rectifiability of those sets, up to the boundary. |
| title | Optimal regularity up to the boundary for Plateau-quasi-minimizers |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2507.13189 |