Liouville系统的鼓泡溶液分布
Profile of bubbling solutions to a Liouville system
摘要：
在物理学、化学和生态学的许多领域中，都有一些模型是用刘维尔系统来描述的。本文首先证明了$\mathbb R^2$中Liouville系统的一个唯一性结果。然后，我们建立了局部定义的Liouville系统在孤立爆破点附近的泡解的一个一致估计。Riemann曲面上Liouville方程组的唯一性结果和局部一致估计是获得其先验估计、度计算公式和存在性结果的重要组成部分.
英文摘要：
In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in $\mathbb R^2$. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial ingredients for obtaining a priori estimate, degree counting formulas and existence results for Liouville systems defined on Riemann surfaces.
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