Density estimates for a nonlocal variational model via the Sobolev inequality

Ovidiu Savin, Enrico Valdinoci

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We consider the minimizers of the energy ∥u∥ H s 2(Ω) +∫ΩW(u) dx, with s ∈ (0, 1/2), where ∥u∥ Hs(Ω) denotes the total contribution from Ω in the H s norm of u, and W is a double-well potential. By using a fractional Sobolev inequality, we give a new proof of the fact that the sublevel sets of a minimizer u in a large ball BR occupy a volume comparable with the volume of B R.

Original languageEnglish
Pages (from-to)2675-2687
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume43
Issue number6
DOIs
Publication statusPublished - 1 Dec 2011
Externally publishedYes

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