Extensions of traces for Sobolev mappings into manifolds at the endpoint p=1

2025/02/24 by Van Schaftingen, Jean, Van Vaerenbergh, Benoît
#46T10 #58D15 (Primary) 46E35 #58J32 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.17245

Abstract

We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in W^{1, 1} (M, N), where M is Riemannian manifold with compact boundary ∂ M and N is a complete Riemannian manifold. The analysis is also applicable to halfspaces and strips. The extension is based on a tiling the domain of the considered applications by suitably chosen dyadic cubes to construct the desired extension. Along the way, we obtain asymptotic characterizations of the L¹-energy of mappings.

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