Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries

Fuente: arXiv
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Main Authors: Azzam, Jonas, Mourgoglou, Mihalis, Villa, Michele
Format: Preprint
Published: 2025
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author Azzam, Jonas
Mourgoglou, Mihalis
Villa, Michele
author_facet Azzam, Jonas
Mourgoglou, Mihalis
Villa, Michele
contents Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the $L^p$ Hajlasz-Sobolev space on the boundary from the space of functions on the domain with $L^p$ norm involving the non-tangential maximal function of the gradient and the conical square function of the Hessian. This fundametally uses the Dorronsoro theorem for UR sets proven in a companion paper.
format Preprint
id arxiv_https___arxiv_org_abs_2511_10137
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries
Azzam, Jonas
Mourgoglou, Mihalis
Villa, Michele
Classical Analysis and ODEs
46E35
Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the $L^p$ Hajlasz-Sobolev space on the boundary from the space of functions on the domain with $L^p$ norm involving the non-tangential maximal function of the gradient and the conical square function of the Hessian. This fundametally uses the Dorronsoro theorem for UR sets proven in a companion paper.
title Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries
topic Classical Analysis and ODEs
46E35
url https://arxiv.org/abs/2511.10137