Minimizers for the fractional Sobolev inequality on domains

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

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0944-2669
• Language: English