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arXiv · 2304.10099

Weighted fractional Sobolev-Poincar\'e inequalities in irregular domains

Yi Xuan
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Abstract

In this paper, we study weighted fractional Sobolev-Poincar\'e inequalities for irregular domains. The weights considered here are distances to the boundary to certain powers, and the domains are the so-called $s$-John domains and $\beta$-H\"older domains. Our main results extend that of Hajlasz-Koskela [J. Lond. Math. Soc. 1998] from the classical weighted Sobolev-Poincar\'e inequality to its fractional counter-part and Guo [Chin. Ann. Math. 2017] from the frational Sobolev-Poincar\'e inequality to its weighted case.

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Yi Xuan. 2023-04-20. Weighted fractional Sobolev-Poincar\'e inequalities in irregular domains. https://arxiv.org/abs/2304.10099

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