Sharp upper bound for a branched transport problem coming from Ginzburg-Landau models
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913116527263744 |
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| author | Cosenza, Alessandro Goldman, Michael Otto, Felix |
| author_facet | Cosenza, Alessandro Goldman, Michael Otto, Felix |
| contents | We consider a branched transport type problem with weakly imposed boundary conditions, which can be seen as a blown-up version of a reduced model for type-I superconductors in the regime of vanishing external magnetic field. We prove that if the irrigated measure is (locally) Ahlfors regular then it is of dimension at most $8/5$ in agreement with the conjecture by Conti, the third author and Serfaty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp upper bound for a branched transport problem coming from Ginzburg-Landau models Cosenza, Alessandro Goldman, Michael Otto, Felix Analysis of PDEs 82D55, 49Q22, 49Q10, 28A80, 49Q20 We consider a branched transport type problem with weakly imposed boundary conditions, which can be seen as a blown-up version of a reduced model for type-I superconductors in the regime of vanishing external magnetic field. We prove that if the irrigated measure is (locally) Ahlfors regular then it is of dimension at most $8/5$ in agreement with the conjecture by Conti, the third author and Serfaty. |
| title | Sharp upper bound for a branched transport problem coming from Ginzburg-Landau models |
| topic | Analysis of PDEs 82D55, 49Q22, 49Q10, 28A80, 49Q20 |
| url | https://arxiv.org/abs/2605.11834 |