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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Bibliographic Details
Published in:Journal of functional analysis Vol. 289; no. 11; p. 111142
Main Authors: Gavioli, Chiara, Happ, Leon, Pagliari, Valerio
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2025
Subjects:
Extension of functions
Manifold constraint
Perforated domain
Trace operator
54C20
55S35
Extension of functions
46E35
Perforated domain
46T10
Manifold constraint
Trace operator
ISSN:0022-1236
Online Access:Get full text
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Summary: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.
ISSN:0022-1236
DOI:10.1016/j.jfa.2025.111142