Partial regularity for the optimal $p$-compliance problem with length penalization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913681926782976 |
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| author | Bulanyi, Bohdan |
| author_facet | Bulanyi, Bohdan |
| contents | We establish a partial $C^{1,α}$ regularity result for minimizers of the optimal $p$-compliance problem with length penalization in any spatial dimension $N\geq 2$, extending some of the results obtained in [Chambolle-Lamboley-Lemenant-Stepanov 17], [Bulanyi-Lemenant 20]. The key feature is that the $C^{1,α}$ regularity of minimizers for some free boundary type problem is investigated with a free boundary set of codimension $N-1$. We prove that every optimal set cannot contain closed loops, and it is $C^{1,α}$ regular at $\mathcal{H}^{1}$-a.e. point for every $p\in (N-1,+\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_04231 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Partial regularity for the optimal $p$-compliance problem with length penalization Bulanyi, Bohdan Analysis of PDEs Optimization and Control 49Q20 We establish a partial $C^{1,α}$ regularity result for minimizers of the optimal $p$-compliance problem with length penalization in any spatial dimension $N\geq 2$, extending some of the results obtained in [Chambolle-Lamboley-Lemenant-Stepanov 17], [Bulanyi-Lemenant 20]. The key feature is that the $C^{1,α}$ regularity of minimizers for some free boundary type problem is investigated with a free boundary set of codimension $N-1$. We prove that every optimal set cannot contain closed loops, and it is $C^{1,α}$ regular at $\mathcal{H}^{1}$-a.e. point for every $p\in (N-1,+\infty)$. |
| title | Partial regularity for the optimal $p$-compliance problem with length penalization |
| topic | Analysis of PDEs Optimization and Control 49Q20 |
| url | https://arxiv.org/abs/2101.04231 |