Scaling limits and regularity results for a class of Ginzburg-Landau systems
Scaling limits and regularity results for a class of Ginzburg-Landau systems
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DOI：
10.1016/s0294-1449(99)80024-9
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发表时间：
1999-07
影响因子：
1.9
通讯作者：
R. Jerrard;H. Soner
中科院分区：
文献类型：
--
作者：
R. Jerrard;H. Soner
我们研究一类抛物线系统，其中包括 Ginzburg-Landau 热流方程，[公式：参见文本] uϵ: Rd→ R2，以及取 Rk 值的函数的一些自然拟线性推广，k ≥ 2。我们证明，对于一般系统的解，能量测度的 ϵ → 0 的极限支持是通过平均曲率演化的余维 k 流形。我们还建立了一些局部正则性结果，这些结果在 ϵ 中一致成立。特别是，我们建立了一般系统的小能量正则性定理，并证明了R2上的通常Ginzburg-Landau方程具有更强的正则性结果。
We study a class of parabolic systems which includes the Ginzburg-Landau heat flow equation, [Formula: see text] for uϵ: 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 ϵ → 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 ϵ. 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.