Calculus of Variations and Geometric Measure Theory

D. Bartolucci - A. Jevnikar - C. S. Lin

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

created by jevnikar on 19 Apr 2018
modified on 21 Aug 2018


Accepted Paper

Inserted: 19 apr 2018
Last Updated: 21 aug 2018

Journal: J. Diff. Eq.
Year: 2018


The aim of this paper is to complete the program initiated in [50], [23] 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