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arXiv · 0903.0381

Profile of bubbling solutions to a Liouville system

Chang-shou Lin·Lei Zhang
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Abstract

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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Chang-shou Lin, Lei Zhang. 2009-03-02. Profile of bubbling solutions to a Liouville system. https://doi.org/10.1016/j.anihpc.2009.09.001

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