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The aim of this paper is to complete the program initiated in [50], [23] andthen carried out by several authors concerning non-degeneracy and uniqueness ofsolutions to mean field equations. In particular, we consider mean fieldequations with general singular data on non-smooth domains. The argument isbased on the Alexandrov-Bol inequality and on the eigenvalues analysis oflinearized singular Liouville-type problems.

Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains