Calculus of Variations and Geometric Measure Theory

D. Bartolucci - A. Jevnikar - Y. Lee - W. Yang

Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data

created by jevnikar on 28 May 2019
modified on 23 Dec 2019


Accepted Paper

Inserted: 28 may 2019
Last Updated: 23 dec 2019

Journal: J. Diff. Eq.
Year: 2019


We are concerned with the mean field equation with singular data on bounded domains. Under suitable non-degeneracy conditions we prove uniqueness and non-degeneracy of bubbling solutions blowing up at singular points. The proof is based on sharp estimates for bubbling solutions of singular mean field equations and suitably defined Pohozaev-type identities.

Keywords: uniqueness, blow-up, Mean field equation, Non-degeneracy, Singular Liouville equations