Γ-convergence for nonlocal phase transitions

Ovidiu Savin, Enrico Valdinoci

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

We discuss the Γ-convergence, under the appropriate scaling, of the energy functional∥u∥Hs(Ω) 2+∫ ΩW(u)dx, with s∈(0,1), where ∥u∥Hs (Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s∈[1/2,1), we show that the energy Γ-converges to the classical minimal surface functional - while, when s∈(0,1/2), it is easy to see that the functional Γ-converges to the nonlocal minimal surface functional.

Original languageEnglish
Pages (from-to)479-500
Number of pages22
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Jan 2012
Externally publishedYes

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