Profile of bubbling solutions to a Liouville system
arXiv:0903.0381 · doi:10.1016/j.anihpc.2009.09.001
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.
32 pages