Density estimates for a variational model driven by the Gagliardo norm

Ovidiu Savin, Enrico Valdinoci

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

We prove density estimates for level sets of minimizers of the energyε2s{norm of matrix}u{norm of matrix}Hs(Ω)2+∫ΩW(u)dx, with s∈(0, 1), where {norm of matrix}u{norm of matrix}Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential.As a consequence we obtain, as ε→0+, the uniform convergence of the level sets of u to either an Hs-nonlocal minimal surface if s∈(0,12), or to a classical minimal surface if s∈[12,1).

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalJournal des Mathematiques Pures et Appliquees
Volume101
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

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