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- W2949536482 abstract "In 1989 Almgren and Lieb proved a rearrangement inequality for the Sobolevspaces of fractional order $W^{s,p}$. When $p=2$ the square of the seminorm in$W^{s,2}$ of an indicator function is the nonlocal perimeter of Caffarelli,Roquejoffre and Savin. In this note we use the Fourier transform to computeexplicitly the nonlocal perimeter of a ball. On one hand, this allows toextract from the inequality of Almgren and Lieb the nonlocal isoperimetricinequality with an explicit constant (which is optimal in view of a result ofFrank and Seiringer). On the other hand, combining such result with D'avila'srefinement of a theorem of Bourgain, Brezis and Mironescu, we show that, in thelimit as $snearrow 1/2$, the nonlocal isoperimetric inequality of Almgren andLieb converges to De Giorgi's isoperimetric inequality." @default.
- W2949536482 created "2019-06-27" @default.
- W2949536482 creator A5007893278 @default.
- W2949536482 date "2019-06-13" @default.
- W2949536482 modified "2023-09-27" @default.
- W2949536482 title "Observations on a theorem of Almgren and Lieb" @default.
- W2949536482 hasPublicationYear "2019" @default.
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