On the existence of extensions for manifold-valued Sobolev maps on perforated domains
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 C2-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case w...
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| Veröffentlicht in: | Journal of functional analysis Jg. 289; H. 11; S. 111142 |
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| Sprache: | Englisch |
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| ISSN: | 0022-1236 |
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| Abstract | 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 C2-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. |
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| AbstractList | 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 C2-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. |
| ArticleNumber | 111142 |
| Author | Pagliari, Valerio Gavioli, Chiara Happ, Leon |
| Author_xml | – sequence: 1 givenname: Chiara surname: Gavioli fullname: Gavioli, Chiara email: chiara.gavioli@cvut.cz organization: Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 16629 Prague 6, Czech Republic – sequence: 2 givenname: Leon orcidid: 0009-0008-2418-4517 surname: Happ fullname: Happ, Leon email: leon.happ@uam.es organization: Departamento de Matemáticas, Universidad Autónoma de Madrid, C/ Francisco Tomás y Valiente 7, 28049 Madrid, Spain – sequence: 3 givenname: Valerio surname: Pagliari fullname: Pagliari, Valerio email: valerio.pagliari@tuwien.ac.at organization: Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria |
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| Cites_doi | 10.1002/cpa.3160400503 10.1016/j.nonrwa.2024.104198 10.1007/s00526-024-02673-0 10.1098/rspa.2001.0864 10.2307/1969265 10.1051/cocv/2009025 10.1007/s00205-019-01418-0 10.1007/978-3-030-01777-4 10.1016/j.na.2021.112316 10.1007/s11784-014-0172-5 10.5802/afst.1675 10.1142/S0218202522500385 10.1137/0523084 10.1007/s00332-008-9033-y 10.1515/acv-2022-0009 10.1007/BF01187897 10.1016/0362-546X(94)90164-3 10.1007/s00205-011-0481-4 10.1142/S0219199722500031 10.1016/0362-546X(92)90015-7 10.1051/m2an/1988220405611 10.1007/BF01671566 10.1016/0022-247X(79)90211-7 10.2140/apde.2021.14.1851 10.1007/s11784-014-0185-0 10.2307/1969989 |
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| Keywords | 54C20 55S35 Extension of functions 46E35 Perforated domain 46T10 Manifold constraint Trace operator |
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| Snippet | Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking... |
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| SubjectTerms | Extension of functions Manifold constraint Perforated domain Trace operator |
| Title | On the existence of extensions for manifold-valued Sobolev maps on perforated domains |
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