| Autor: |
Hugo Tavares, Alessandro Zilio |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Mathematics in Engineering, Vol 3, Iss 1, Pp 1-31 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2640-3501 |
| DOI: |
10.3934/mine.2021002/fulltext.html |
| Popis: |
We study a rather broad class of optimal partition problems with respect to monotone and coercive functional costs that involve the Dirichlet eigenvalues of the partitions. We show a sharp regularity result for the entire set of minimizers for a natural relaxed version of the original problem, together with the regularity of eigenfunctions and a universal free boundary condition. Among others, our result covers the cases of the following functional costs \[ (\omega_1, \dots, \omega_m) \mapsto \sum_{i=1}^{m} \left( \sum_{j=1}^{k_i} \lambda_{j}(\omega_i)^{p_i}\right)^{1/p_i}, \quad \prod_{i=1}^{m} \left( \prod_{j=1}^{k_i} \lambda_{j}(\omega_i)\right), \quad \prod_{i=1}^{m} \left( \sum_{j=1}^{k_i} \lambda_{j}(\omega_i)\right) \] where $(\omega_1, \dots, \omega_m)$ are the sets of the partition and $\lambda_{j}(\omega_i)$ is the $j$-th Laplace eigenvalue of the set $\omega_i$ with zero Dirichlet boundary conditions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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