On the local character of the extension of traces for Sobolev mappings - Van Schaftingen, Jean (Topological Methods in Nonlinear Analysis, 2026)
We prove that a mapping u M’→ N, where M’ and N are compact Riemannian manifolds, is the trace of a Sobolev mapping U M’ × [0, 1) → N if and only if it is on some open covering of M’. In the global case where M is a compact Riemannian manifold with boundary, this implies that the analytical obstructions to the extension of a mapping u M→ N to some Sobolev mapping U M → N are purely local.