Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.11690 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.