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arXiv · 1707.00131

Minimizers for the fractional Sobolev inequality on domains

Rupert L. Frank·Tianling Jin·Jingang Xiong
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Abstract

We consider a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.

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Rupert L. Frank, Tianling Jin, Jingang Xiong. 2017-07-01. Minimizers for the fractional Sobolev inequality on domains. https://arxiv.org/abs/1707.00131

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