| 摘要: |
| 本本文研究了由一类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-Schauder不动点定理，我们得到了这个方程在R2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C2,α解的存在性. |
| 关键词: Hermitian Yang-Mills度量 Ck-估计 边值问题 |
| DOI： |
| 分类号:O186 |
| 基金项目:Supported by the National Natural Science Foundation of China (11701426). |
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| A SEMILINEAR PARTIAL DIFFERENTIAL EQUATION INDUCED BY HERMITIAN YANG-MILLS METRICS |
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LI Yu-xuan, ZHOU Wu-bin
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School of Mathematical Sciences, Tongji University, Shanghai 200082, China
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| Abstract: |
| 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 C2 global solution in R2 and the existence of C2, α solution of the Dirichlet problem in any bounded domain. |
| Key words: Hermitian Yang-Mills metric Ck-estimates boundary value problems |
