New dimensional bounds for a branched transport problem
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911275619975168 |
|---|---|
| author | Cosenza, Alessandro Goldman, Michael Koser, Melanie |
| author_facet | Cosenza, Alessandro Goldman, Michael Koser, Melanie |
| contents | We consider a branched transport problem with weakly imposed boundary conditions. This problem arises as a reduced model for pattern formation in type-I superconductors. For this model, it is conjectured that the dimension of the boundary measure is non-integer. We prove this conjecture in a simplified 2D setting, under the (strong) assumption of Ahlfors regularity of the irrigated measure. This work is the first rigorous proof of a singular behaviour for irrigated measures resulting from minimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New dimensional bounds for a branched transport problem Cosenza, Alessandro Goldman, Michael Koser, Melanie Analysis of PDEs We consider a branched transport problem with weakly imposed boundary conditions. This problem arises as a reduced model for pattern formation in type-I superconductors. For this model, it is conjectured that the dimension of the boundary measure is non-integer. We prove this conjecture in a simplified 2D setting, under the (strong) assumption of Ahlfors regularity of the irrigated measure. This work is the first rigorous proof of a singular behaviour for irrigated measures resulting from minimality. |
| title | New dimensional bounds for a branched transport problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.14547 |