Partial regularity of weak solutions for Landau-Lifshitz system with potential  

作　　者：CHU YuMing LIU XianGao 

机构地区：[1]Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China [2]Institute of Mathematics,Fudan University,Shanghai 200433,China

出　　处：《Science China Mathematics》2009年第5期981-990,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10631020, 60850005);the Natural Science Foundation of Zhejiang Province (Grant No. D7080080)

摘　　要：In this note, we prove the partial regularity of stationary weak solutions for the Landau- Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey's energy to avoid the difficulties by blowing up.In this note, we prove the partial regularity of stationary weak solutions for the Landau-Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey’s energy to avoid the difficulties by blowing up.

关 键 词：partial regularity POTENTIAL Landau-Lifshitz system 35K55 35D10 

分 类 号：O175[理学—数学]