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arXiv · 2608.28807

On the measure of the boundary of a Haj\l{}asz-Sobolev $(M^{1,p},M^{1,q})$-extension domain

Ryan Alvarado·Riddhi Mishra
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Abstract

We prove that the boundary of every bounded $(M^{1,p},M^{1,q})$-extension domain in a $Q$-doubling metric measure space has measure zero whenever $0<q<p<\infty$, with the additional restriction that $p<qQ/(Q-q)$ if $q<Q$.

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Ryan Alvarado, Riddhi Mishra. 2026-08-28. On the measure of the boundary of a Haj\l{}asz-Sobolev $(M^{1,p},M^{1,q})$-extension domain. https://arxiv.org/abs/2608.28807

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