Blow-up analysis of stationary solutions to a Liouville-type equation in 3D

In this paper, we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation: [Formula: see text] where [Formula: see text] is an open set. By improving the partial regularity estimates obtained by the first author in F. Da Lio [Partial regularity for stationary solutions to Liouville-type equation in dimension 3, Comm. Partial Differential Equations 33(10–12) (2008) 1890–1910] for Eq.(1) we succeed in performing a blow-up analysis without Morrey-type assumptions on the solutions [Formula: see text] and on the nonlinearity [Formula: see text]