Nonexistence of Smooth Axially Symmetric Harmonic Maps from B^3 into S^2
Nonexistence of Smooth Axially Symmetric Harmonic Maps from B^3 into S^2
摘要
Inspired by the construction of blow-up solutions of the heat flow of harmonic maps from D^2 into S^2 via maximum principle （Chang et al., J. Diff. Geom., 36, 1992, pp. 507-515.） we provide examples of nonexistence of smooth axially symmetric harmonic maps from B^3 into S^2 with smooth boundary maps of degree zero.
参考文献10
-
1Chang K. C., Ding W. Y., Ye R. G., Finite-time blow-up of the heat flow of harmonic maps from surfaces. J. Diff. Geom., 36 (2) (1992), 507-515.
-
2Schoen R., Uhlenbeck K., A regularity theory for hamonic maps. J. Diff. Geom., 17 (1982), 307-335.
-
3Brezis H., Coron J. M., Lieb E., Harmonic maps with defects. Comm. Math. Phys., 107 (1986), 649-705.
-
4Bethuel F., Brezis H., Coron J. M., Relaxed energies for harmonic maps, in Variational Methods (Paris, 1988). Progr. Nonlinear Differential Equations Appl., 4 (1990), Birkhauser, Boston, 37-52.
-
5Bethuel F., Brezis H., Regularity of minimizers of relaxed problems for harmonic maps. J. Funct. Anal., 101 (1991), 145-161.
-
6Giaquinta M., Modica G., Soucek J., The Dirichlet energy of mappings with values into the sphere. Manuscripta Math., 65 (1989), 489-507.
-
7Giaquinta M., Modica G., Soucek J., Cartesian currents and variational problems for mappings into spheres. Ann. Sc. Norm. Sup. Pisa, (1990), 393-485.
-
8Hardt R., Lin F. H., A remark on H1 mappings. Manuscripta Math., 56 (1986), 1-10.
-
9Zhang D., The existence of nonminimal regular harmonic maps from B3 to S2. Ann. Sc. Norm. Sup. Pisa CI. Sci., 16(4) (1989), 355-365.
-
10Hardt R., Axially symmetric harmonic maps, in Nematics (Orsay, 1990), 179-187. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 332, Kluwer Acad. Publ., Dordrecht, (1991), 179-187.
-
1周爱民.从能力到素质——谈谈个人能力的系统性[J].程序员,2010(1):60-61.
-
2任晓宾.论博弈在航运竞争与合作中的应用[J].中国水运,2005(12):32-33.
-
3达雷尔·里格比,唐麦,柴文静（采访整理）.寻找安渡危机的支点[J].21世纪商业评论,2009(7):100-104.
-
4樊浩,刘冠男,朱林,李刚.基于变异系数与TOPSIS的信息作战行动方案优选方法研究[J].舰船电子工程,2013,33(3):26-28. 被引量：2
-
5张侨平.香港和台湾高中数学课程纲要比较研究[J].数学教学,2010(9):14-19. 被引量：3
-
6K.Ozeki,T.Hoshino,H.Aoki,T.Masuzawa.Phase Composition of Sputtered Film from a Mixture Target of Hydroxyapatite and Strontium-apatite[J].Journal of Materials Science & Technology,2013,29(1):1-6.
-
7毛春华.一种风险型决策的效用模型及其应用[J].赤峰学院学报（自然科学版）,2015,31(20):10-12.
-
8鞠强.二元平衡决策[J].经济管理,2003,29(7):30-33.
-
9陈遵银,王超勇,毕嗣民.导弹反舰训练效果灰色评估模型研究[J].航空计算技术,2016,46(6):43-45. 被引量：1
-
10耿修林.基于正交设计原理的新型干法水泥生产过程的优化[J].数理统计与管理,2013,32(1):18-27.
