Bump solutions for the mesoscopic Allen-Cahn equation in periodic media

Matteo Novaga, Enrico Valdinoci

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Given a double-well potential F, a ℤn-periodic function H, small and with zero average, and ε > 0, we find a large R, a small δ and a function Hε which is ε-close to H for which the following two problems have solutions:1. Find a set Eε,R whose boundary is uniformly close to ∂ BR and has mean curvature equal to -Hε at any point, 2. Find u = uε,R,δ solving such that uε,R,δ goes from a δ-neighborhood of +1 in BR to a δ-neighborhood of -1 outside BR.

Original languageEnglish
Pages (from-to)37-49
Number of pages13
JournalCalculus of Variations and Partial Differential Equations
Volume40
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011
Externally publishedYes

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