Minimizers for the fractional Sobolev inequality on domains

Frank, Rupert L. ; Jin, Tianling und Xiong, Jingang (2018): Minimizers for the fractional Sobolev inequality on domains. In: Calculus of Variations and Partial Differential Equations, Bd. 57, Nr. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0944-2669
• Sprache: Englisch