Scaling limits and regularity results for a class of Ginzburg-Landau systems

Robert L. Jerrard, Halil Mete Soner

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We study a class of parabolic systems which includes the Ginzburg-Landau heat flow equation, ut - Δu + 1/∈2(|u|2 - 1)u∈ = 0 for u : Rd → R2, as well as some natural quasilinear generalizations for functions taking values in Rk, k ≥ 2. We prove that for solutions of the general system, the limiting support as ∈ → 0 of the energy measure is a codimension k manifold which evolves via mean curvature. We also establish some local regularity results which hold uniformly in ∈. In particular, we establish a small-energy regulity theorem for the general system, and we prove a stronger regularity result for the usual Ginzburg-Landau equation on R2.

Original languageEnglish (US)
Pages (from-to)423-466
Number of pages44
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume16
Issue number4
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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