On the existence of extensions for manifold-valued Sobolev maps on perforated domains

2024/03/18 by Chiara Gavioli, Gavioli, Chiara, Leon Happ +3
Mathematics · #46E35 #46T10 #54C20 #55S35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2403.11690

openalex publication_date 2024/03/18 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28

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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