Regularity of harmonic maps with the potential

被引:0
作者
Yuming Chu
Xiangao Liu
机构
[1] Huzhou Teachers College,Department of Mathematics
[2] Fudan University,Institute of Mathematics
来源
Science in China Series A | 2006年 / 49卷
关键词
harmonic map; partial regularity; potential;
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中图分类号
学科分类号
摘要
The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.
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页码:599 / 610
页数:11
相关论文
共 21 条
[1]  
Fardoun A.(1997)Harmonic maps with potential Calc. Var. Partial Differential Equations 5 183-197
[2]  
Ratto A.(1995)Everywhere discontinuous harmonic maps into spheres Acta Math. 175 197-226
[3]  
Rivière T.(1991)Partial regularity for stationary harmonic maps into spheres Arch. Rational Mech. Anal. 116 101-113
[4]  
Evans L. C.(1993)On the singular set of stationary harmonic maps Manuscripta Math. 78 417-443
[5]  
Bethuel F.(2003)Heat flow for Calc. Var. Partial Differential Equations 16 1-16
[6]  
Fardoun A.(2002)-harmonic maps with small initial data Indiana Univ. Math. J. 51 1305-1320
[7]  
Regbaoui R.(2000)Heat flow for Ann. Global Anal. Geom. 18 555-567
[8]  
Fardoun A.(1984)-harmonic maps between compact Riemannian manifolds J. Differential Equations 51 126-150
[9]  
Regbaoui R.(1992)On the heat flow for harmonic maps with potential J. Reine Angew. Math. 431 7-64
[10]  
Fardoun A.(1991)Regularity for a more general class of quasilinear elliptic equations C. R. Acad. Sci. Paris 312 591-596