Chang-shou Lin, Lei Zhang
Published 2009-03-02Version 1
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.
On Liouville systems at critical parameters, Part 1: one bubble
Existence and uniqueness results for a nonlinear stationary system
Uniqueness of bubbling solutions of mean field equations with non-quantized singularities
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