Symmetry of the Ginzburg Landau Minimizer in a Disc
Symmetry of the Ginzburg Landau Minimizer in a Disc
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DOI：
10.1007/978-3-642-55925-9_53
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发表时间：
1994
影响因子：
1
通讯作者：
E. Lieb;M. Loss
中科院分区：
文献类型：
--
作者：
E. Lieb;M. Loss
研究了二维圆盘上向量场的Ginzburg-Landau能量极小化问题。这是向量场最小化问题的最简单的非平凡例子，目的是证明能量最小化具有问题的完全几何对称性。对涉及真实的值函数的类似问题有用的标准方法不能应用于这种情况。我们的主要结果是对称域类中的极小元是稳定的，即，第二变分算子的特征值都是非负的。
The Ginzburg-Landau energy minimization problem for a vector field on a two dimensional disc is analyzed. This is the simplest nontrivial example of avector fieldminimization problem and the goal is to show that the energy minimizer has the full geometric symmetry of the problem. The standard methods that are useful for similar problems involving real valuedfunctionscannot be applied to this situation. Our main result is that the minimizer in the class of symmetric fields is stable, i.e., the eigenvalues of the second variation operator are all nonnegative.