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

Jonas Azzam; Mihalis Mourgoglou; Michele Villa

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

Classical Analysis and ODEs 2025-11-14 v1

Authors: Jonas Azzam , Mihalis Mourgoglou , Michele Villa

Abstract

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.

Keywords

recommendation systems generative models pre-trained models advertising policy optimization

Cite

@article{arxiv.2511.10137,
  title  = {Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries},
  author = {Jonas Azzam and Mihalis Mourgoglou and Michele Villa},
  journal= {arXiv preprint arXiv:2511.10137},
  year   = {2025}
}

Comments

This articles comes from the preprint arXiv:2306.13017, which we split in two for readability's sake

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

Abstract

Keywords

Cite

Comments

Related papers