Abstract
We study a class of parabolic systems which includes the Ginzburg-Landau heat flow equation, u∈t - 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 language | English (US) |
---|---|
Pages (from-to) | 423-466 |
Number of pages | 44 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Jan 1 1999 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Mathematical Physics
- Applied Mathematics