Published Paper

Inserted: 12 nov 2024
Last Updated: 31 jul 2025

Journal: Journal of Functional Analysis
Volume: 289
Number: 11
Pages: 111142
Year: 2025
Doi: 10.1016/j.jfa.2025.111142

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 $C^2$-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.

Keywords: extension of functions, perforated domain, manifold constraint, trace operator