Partial regularity for the optimal $p$-compliance problem with length penalization
| Autor: | Bulanyi, Bohdan |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We establish a partial $C^{1,\alpha}$ 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 $C^{1,\alpha}$ 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 $C^{1,\alpha}$ regular at $\mathcal{H}^{1}$-a.e. point for every $p\in (N-1,+\infty)$. Comment: 42 pages, 2 figures. arXiv admin note: text overlap with arXiv:1911.09240 |
| Databáze: | arXiv |
| Externí odkaz: |
|