Coercivity and Gamma-convergence of the $p$-energy of sphere-valued Sobolev maps
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917959716306944 |
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| author | Caselli, Michele Freguglia, Mattia Picenni, Nicola |
| author_facet | Caselli, Michele Freguglia, Mattia Picenni, Nicola |
| contents | We consider sequences of maps from an $(n+m)$-dimensional domain into the $(n-1)$-sphere, which satisfy a natural $p$-energy growth, as $p$ approaches $n$ from below. We prove that, up to subsequences, the Jacobians of such maps converge in the flat topology to an integral $m$-current, and that the $p$-energy Gamma-converges to the mass of the limit current.
As a corollary, we deduce that the Jacobians of $p$-energy minimizing maps converge to an integral $m$-current that is area-minimizing in a suitable cobordism class, depending on the boundary datum. Moreover, we obtain new estimates for the minimal $p$-energy of maps with prescribed singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coercivity and Gamma-convergence of the $p$-energy of sphere-valued Sobolev maps Caselli, Michele Freguglia, Mattia Picenni, Nicola Analysis of PDEs Differential Geometry Functional Analysis 49J45, 49Q20, 58K45, 58E20 We consider sequences of maps from an $(n+m)$-dimensional domain into the $(n-1)$-sphere, which satisfy a natural $p$-energy growth, as $p$ approaches $n$ from below. We prove that, up to subsequences, the Jacobians of such maps converge in the flat topology to an integral $m$-current, and that the $p$-energy Gamma-converges to the mass of the limit current. As a corollary, we deduce that the Jacobians of $p$-energy minimizing maps converge to an integral $m$-current that is area-minimizing in a suitable cobordism class, depending on the boundary datum. Moreover, we obtain new estimates for the minimal $p$-energy of maps with prescribed singularities. |
| title | Coercivity and Gamma-convergence of the $p$-energy of sphere-valued Sobolev maps |
| topic | Analysis of PDEs Differential Geometry Functional Analysis 49J45, 49Q20, 58K45, 58E20 |
| url | https://arxiv.org/abs/2503.14142 |