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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.11690 |
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| _version_ | 1866915430968328192 |
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| author | Gavioli, Chiara Happ, Leon Pagliari, Valerio |
| author_facet | Gavioli, Chiara Happ, Leon Pagliari, Valerio |
| contents | Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected $C^2$-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case with a retraction argument that heavily relies on the topological properties of the manifold. With the ultimate goal of providing necessary conditions for the existence of extensions for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the existence of extensions for manifold-valued Sobolev maps on perforated domains Gavioli, Chiara Happ, Leon Pagliari, Valerio Analysis of PDEs 54C20, 46T10, 46E35, 55S35 Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected $C^2$-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case with a retraction argument that heavily relies on the topological properties of the manifold. With the ultimate goal of providing necessary conditions for the existence of extensions for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such functions. |
| title | On the existence of extensions for manifold-valued Sobolev maps on perforated domains |
| topic | Analysis of PDEs 54C20, 46T10, 46E35, 55S35 |
| url | https://arxiv.org/abs/2403.11690 |