Blow-up Analysis of Stationary Solutions to a Liouville-Type Equation in 3-D

Abstract

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation $-\hat{I}”u=e^{u}in\hat{I}\text{c◯}$, where $\hat{I}\text{c◯}$ is an open set of $R^3$. By improving the partial regularity estimates obtained by the first author for the above equation, we succeed in performing a blow-up analysis without Morrey-type assumptions on the solutions $u$ and on the nonlinearity $e^u.$

29 pages