Partial regularity for the Landau-Lifshitz system
Partial regularity for the Landau-Lifshitz system
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DOI：
10.1007/s00526-003-0231-z
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发表时间：
2004-06
影响因子：
2.1
通讯作者：
Xian-gao Liu
中科院分区：
文献类型：
--
作者：
Xian-gao Liu
本文研究了铁磁自旋链Landau-Lifshitz系统从m维流形M到R ~ 3的单位球S ~ 2的定态弱解的部分正则性. Landau-Lifshitz系统在外观上非常类似于调和映射到球面的热流。然而，单调性不等式，这在获得部分正则性的重要作用，在这种情况下不成立。这成为了规律性的一个巨大障碍。本文得到了一个推广的单调性不等式，并求出了Landau-Lifshitz系统平稳弱解的奇异集。
The aim of this work is to consider the partial regularity for the stationary weak solutions to the Landau-Lifshitz system of Ferromagnetic spin chain from am-dimensional manifoldMinto the unit sphereS2ofR3. The Landau-Lifshitz system is in appearance very similar to the heat flows of harmonic maps into sphere. However the monotonicity inequality, which plays an important role in getting partial regularity, does not hold in this case. This becomes a large barrier to regularity. In the present paper we get a generalized monotonicity inequality, and find the singular set of the stationary weak solutions of Landau-Lifshitz system.