Equi-integrable approximation of Sobolev mappings between manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914374252232704 |
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| author | Van Schaftingen, Jean |
| author_facet | Van Schaftingen, Jean |
| contents | We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable $W^{1, p}$-Sobolev energy can always be strongly approximated by smooth maps, giving a counterpart of Hang's density result in $W^{1, 1}$ for the Sobolev space $W^{1, p}$ with integer $p \ge 2$. Our result extends to higher-order Sobolev spaces and is straightforward in fractional Sobolev spaces. We also provide a proof based on the weak continuity of Jacobians in the cases where the cohomological criterion of Bethuel, Demengel, Colon and Hélein applies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equi-integrable approximation of Sobolev mappings between manifolds Van Schaftingen, Jean Analysis of PDEs Classical Analysis and ODEs 58D15 (Primary) 46E35, 46T10, 58C25 (Secondary) We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable $W^{1, p}$-Sobolev energy can always be strongly approximated by smooth maps, giving a counterpart of Hang's density result in $W^{1, 1}$ for the Sobolev space $W^{1, p}$ with integer $p \ge 2$. Our result extends to higher-order Sobolev spaces and is straightforward in fractional Sobolev spaces. We also provide a proof based on the weak continuity of Jacobians in the cases where the cohomological criterion of Bethuel, Demengel, Colon and Hélein applies. |
| title | Equi-integrable approximation of Sobolev mappings between manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs 58D15 (Primary) 46E35, 46T10, 58C25 (Secondary) |
| url | https://arxiv.org/abs/2511.20064 |