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arXiv · 2511.10137

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

Jonas Azzam·Mihalis Mourgoglou·Michele Villa
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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.

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Jonas Azzam, Mihalis Mourgoglou, Michele Villa. 2025-11-13. Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries. https://arxiv.org/abs/2511.10137

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