On the best constant in the nonlocal isoperimetric inequality of Almgren and Lieb

  • Nicola Garofalo

    Università di Padova, Italy
On the best constant in the nonlocal isoperimetric inequality of Almgren and Lieb cover
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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