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

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation $-\mathrm{\Delta }u=e^{u}in\mathrm{\Omega }$, where $\mathrm{\Omega }$ 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 $e^u\mathrm{.}$