Regularity for the planar optimal p-compliance problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909480995782656 |
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| author | Bulanyi, Bohdan Lemenant, Antoine |
| author_facet | Bulanyi, Bohdan Lemenant, Antoine |
| contents | In this paper we prove a partial $C^{1,α}$ regularity result in dimension $N=2$ for the optimal $p$-compliance problem, extending for $p\not = 2$ some of the results obtained by A. Chambolle, J. Lamboley, A. Lemenant, E. Stepanov (2017). Because of the lack of good monotonicity estimates for the $p$-energy when $p\not = 2$, we employ an alternative technique based on a compactness argument leading to a $p$-energy decay at any flat point. We finally obtain that every optimal set has no loop, is Ahlfors regular, and $C^{1,α}$ at $\mathcal{H}^1$-a.e. point for every $p \in (1 ,+\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_09240 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Regularity for the planar optimal p-compliance problem Bulanyi, Bohdan Lemenant, Antoine Optimization and Control Analysis of PDEs 49Q20, 35J92 In this paper we prove a partial $C^{1,α}$ regularity result in dimension $N=2$ for the optimal $p$-compliance problem, extending for $p\not = 2$ some of the results obtained by A. Chambolle, J. Lamboley, A. Lemenant, E. Stepanov (2017). Because of the lack of good monotonicity estimates for the $p$-energy when $p\not = 2$, we employ an alternative technique based on a compactness argument leading to a $p$-energy decay at any flat point. We finally obtain that every optimal set has no loop, is Ahlfors regular, and $C^{1,α}$ at $\mathcal{H}^1$-a.e. point for every $p \in (1 ,+\infty)$. |
| title | Regularity for the planar optimal p-compliance problem |
| topic | Optimization and Control Analysis of PDEs 49Q20, 35J92 |
| url | https://arxiv.org/abs/1911.09240 |