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arxiv: 1707.00131 · v1 · pith:YIBCWP3Nnew · submitted 2017-07-01 · 🧮 math.AP · math.FA

Minimizers for the fractional Sobolev inequality on domains

Rupert L. Frank , Tianling Jin , Jingang Xiong This is my paper
classification 🧮 math.AP math.FA
keywords domainsinequalitysobolevfractionalattainedbestboundedclass
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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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