一类由Hermitian Yang-Mills度量导出的半线性偏微分方程  

SEMILINEAR PARTIAL DIFFERENTIAL EQUATION INDUCED BY HERMITIAN YANG-MILLS METRICS

作　　者：李宇萱 周武斌 LI Yu-xuan;ZHOU Wu-bin(School of Mathematical Sciences,Tongji University,Shanghai 200082,China)

机构地区：[1]同济大学数学科学学院,上海200082

出　　处：《数学杂志》2023年第4期283-287,共5页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11701426)。

摘　　要：本文研究了由一类Hermitian Yang-Mills度量的极限行为所导出的半线性方程的边值问题与全局解的径向对称性质.使用极大值原理与Leray-Schhauder不动点定理,我们得到了这个方程在R^(2)平面中全局C2解的径向对称性与这个方程的Dirichlet问题在任意有界区域内C^(2,α)解的存在性.In this paper,we investigate the boundary value problem and the radial symmetry of the global solution of a semilinear partial differential equation induced by studying the limiting behaviour of Hermitian Yang-Mills metrics.By applying maximum principle and Leray-Schauder fixed point theorem,we obtain the radial symmetry of the C^(2,α) global solution in R2 and the existence of C^(2).αsolution of the Dirichlet problem in any bounded domain.

关 键 词：Hermitian Yang-Mills度量 C^(k)-估计 边值问题 

分 类 号：O186[理学—数学]