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Bibliographic Details
Main Authors: Van Schaftingen, Jean, Van Vaerenbergh, Benoît
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.17245
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Table of Contents:
  • 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 $\partial M$ 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 $L^1$-energy of mappings.