Isoperimetric inequalities for the fractional composite membrane problem
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917901373538304 |
|---|---|
| author | Ghosh, Mrityunjoy |
| author_facet | Ghosh, Mrityunjoy |
| contents | In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue of the renowned Faber-Krahn inequality for the fractional composite membrane problem. Next, we investigate an isoperimetric inequality for the first eigenvalue of the fractional composite membrane problem on the intersection of two domains-a problem that was first studied by Lieb [23] for the Laplacian. Similar results in the local case were previously obtained by Cupini-Vecchi [9] for the composite membrane problem. Our findings provide further insights into the fractional setting, offering a new perspective on these classical inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoperimetric inequalities for the fractional composite membrane problem Ghosh, Mrityunjoy Analysis of PDEs Optimization and Control Spectral Theory 35R11, 35P15, 49Q10 In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue of the renowned Faber-Krahn inequality for the fractional composite membrane problem. Next, we investigate an isoperimetric inequality for the first eigenvalue of the fractional composite membrane problem on the intersection of two domains-a problem that was first studied by Lieb [23] for the Laplacian. Similar results in the local case were previously obtained by Cupini-Vecchi [9] for the composite membrane problem. Our findings provide further insights into the fractional setting, offering a new perspective on these classical inequalities. |
| title | Isoperimetric inequalities for the fractional composite membrane problem |
| topic | Analysis of PDEs Optimization and Control Spectral Theory 35R11, 35P15, 49Q10 |
| url | https://arxiv.org/abs/2501.05320 |