On the local character of the extension of traces for Sobolev mappings
(2026) Topological Methods in Nonlinear Analysis — Vol. 67, p. 69-86 (2026)
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- Abstract
- We prove that a mapping $u \colon \mathcal{M}'\to \mathcal{N}$, where $\mathcal{M}'$ and $ \mathcal{N}$ are compact Riemannian manifolds, is the trace of a Sobolev mapping $U \colon \mathcal{M}' \times [0, 1) \to \mathcal{N}$ if and only if it is on some open covering of $\mathcal{M}'$. In the global case where $\mathcal{M}$ is a compact Riemannian manifold with boundary, this implies that the analytical obstructions to the extension of a mapping $u \colon \partial \mathcal{M}\to \mathcal{N}$ to some Sobolev mapping $U \colon \mathcal{M} \to \mathcal{N}$ are purely local.
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Van Schaftingen, J. (2026). On the local character of the extension of traces for Sobolev mappings. Topological Methods in Nonlinear Analysis, 67, 69-86. https://doi.org/10.12775/TMNA.2026.006 (Original work published 2026)