Inserted: 19 apr 2018
Last Updated: 19 apr 2018
The aim of this paper is to complete the program initiated in ,  and then carried out by several authors concerning non-degeneracy and uniqueness of solutions to mean field equations. In particular, we consider mean field equations with general singular data on non-smooth domains. The argument is based on the Alexandrov-Bol inequality and on the eigenvalues analysis of linearized singular Liouville-type problems.
Keywords: uniqueness results, Singular Liouville-type equations, Alexandrov-Bol inequality, Singular Mean field equations, Non-degeneracy