On the best constant in the nonlocal isoperimetric inequality of Almgren and Lieb
Nicola Garofalo
Università di Padova, Italy
Abstract
In 1989 Almgren and Lieb proved a rearrangement inequality for the Sobolev spaces of fractional order . The case of their result implies the nonlocal isoperimetric inequality
where indicates the fractional -perimeter, and is the unit ball in . In this note we explicitly compute the best constant, and show that for any , one has
Cite this article
Nicola Garofalo, On the best constant in the nonlocal isoperimetric inequality of Almgren and Lieb. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 2, pp. 465–470
DOI 10.4171/RLM/900