Limiting domain wall energy for a problem related to micromagnetics

Tristan Rivière, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We study the asymptotic limit of a family of functionals related to the theory of micromagnetics in two dimensions. We prove a compactness result for families of uniformly bounded energy. After studying the corresponding one-dimensional profiles, we exhibit the Γ-limit ("wall energy"), which is a variational problem on the folding of solutions of the eikonal equation |∇g| = 1. We prove that the minimal wall energy is twice the perimeter.

Original languageEnglish (US)
Pages (from-to)294-338
Number of pages45
JournalCommunications on Pure and Applied Mathematics
Volume54
Issue number3
DOIs
StatePublished - Mar 2001

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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