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Frank, Rupert L.; Jin, Tianling; Xiong, Jingang (2018): Minimizers for the fractional Sobolev inequality on domains. In: Calculus of Variations and Partial Differential Equations, Vol. 57, No. 2, 43
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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.