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arXiv · 2507.07072

Sobolev Versus Homogeneous Sobolev II

Pekka Koskela·Riddhi Mishra·Zheng Zhu
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Abstract

We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents $p$ and $q$, we construct a $(W^{1, p}, W^{1, q})$-extension domain which is not an $(L^{1, p}, L^{1, q})$-extension domain.

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Pekka Koskela, Riddhi Mishra, Zheng Zhu. 2025-07-09. Sobolev Versus Homogeneous Sobolev II. https://arxiv.org/abs/2507.07072

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