The boundary value problem for Yang-Mills-Higgs fields

被引：2
|
作者：
Ai, Wanjun [1 ,2 ]
Song, Chong [3 ]
Zhu, Miaomiao [2 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China
[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 58卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Yang-Mills-Higgs; Free boundary; Neumann boundary; Blow-up; Regularity; NON-MINIMAL SOLUTION; HARMONIC MAPS; EXISTENCE; CONNECTIONS; EQUATIONS;
D O I：
10.1007/s00526-019-1587-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show the existence of Yang-Mills-Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the convergence and blow-up behavior of a sequence of Sacks-Uhlenbeck type alpha-YMH fields as alpha -> 1. For alpha>1, some regularity results for alpha-YMH field are shown. This is achieved by showing a regularity theorem for more general coupled systems, which extends the classical results of Ladyzhenskaya-Ural'ceva and Morrey.
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页数：37
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