The extension of traces for Sobolev mappings between manifolds

2024/03/27 by Jean Van Schaftingen, Van Schaftingen, Jean · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2403.18738

Abstract

The compact Riemannian manifolds M and N for which the trace operator from the first-order Sobolev space of mappings \smashW^{1, p} (M, N) to the fractional Sobolev-Slobodecki\uı space \smash\smashW^{1 - 1/p, p} (∂ M, N) is surjective when 1 < p < dim M are characterised. The traces are extended using a new construction which can be carried out assuming the absence of the known topological and analytical obstructions. When p ≥ dim M the same construction provides a Sobolev extension with linear estimates for maps that have a continuous extension, provided that there are no known analytical obstructions to such a control.

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