Lower bounds for generalized Ginzburg-Landau functionals

被引：140

作者：

Jerrard, RL ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1999年 / 30卷 / 04期

关键词：

Ginzburg-Landau functional; lower bounds; energy concentration; compactness;

D O I：

10.1137/S0036141097300581

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study properties of Ginzburg-Landau functionals I-U(epsilon)(.), defined for functions u is an element of W-1,W-n (U; R-n), where U subset of R-n. In particular, we establish lower bounds relating the energy I-U(epsilon)(u) to the Brouwer degree of u, and we prove under additional hypotheses that the energy concentrates on a small number of small sets. As a consequence we deduce some compactness theorems. Such estimates are useful in studying Ginzburg-Landau-type PDEs associated with the functional I-U(epsilon).

引用

页码：721 / 746

页数：26

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