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arXiv · 2606.17738

Sobolev extensions, interpolation inequalities and consequences

Rupert L. Frank·Pekka Koskela·Riddhi Mishra
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Abstract

We prove Sobolev interpolation inequalities on extension domains that have a form reminiscent of the corresponding whole-space inequalities. This form is crucial in certain applications, which we discuss as well. The technical key ingredient is the notion of a Lebesgue $W^{1,p}$-extension domain, which we introduce here, and our proof that, for $1<p<\infty$, any $W^{1,p}$-extension domain is a Lebesgue $W^{1,p}$-extension domain.

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Rupert L. Frank, Pekka Koskela, Riddhi Mishra. 2026-06-16. Sobolev extensions, interpolation inequalities and consequences. https://arxiv.org/abs/2606.17738

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