An extension operator for manifold-valued Sobolev maps on perforated domains. arXiv:2403.11690
Preprint, arXiv:2403.11690 [math.AP] (2024).
Summary: Motivated by manifold-constrained homogenization problems, we construct an extension operator 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 suitable extension operators for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such functions.
MSC:
| 54C20 | Extension of maps |
| 46T10 | Manifolds of mappings |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 55S35 | Obstruction theory in algebraic topology |
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