Existence and Regularity of Minimizers for a Plateau Approximation Problem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866912890430160896 |
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| author | Machefert, Eve |
| author_facet | Machefert, Eve |
| contents | In this paper, we study the functional introduced by the author in collaboration with Bonnivard, Bretin, and Lemenant, which is designed to approximate Plateau's problem. We establish the existence of a minimizer and prove its H{ö}lder regularity. Our results may be viewed as a generalization to higher-dimensional surfaces of the one-dimensional work of Bonnivard, Lemenant, and Millot on the approximation of the Steiner problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08476 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and Regularity of Minimizers for a Plateau Approximation Problem Machefert, Eve Analysis of PDEs In this paper, we study the functional introduced by the author in collaboration with Bonnivard, Bretin, and Lemenant, which is designed to approximate Plateau's problem. We establish the existence of a minimizer and prove its H{ö}lder regularity. Our results may be viewed as a generalization to higher-dimensional surfaces of the one-dimensional work of Bonnivard, Lemenant, and Millot on the approximation of the Steiner problem. |
| title | Existence and Regularity of Minimizers for a Plateau Approximation Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.08476 |