Calculus of Variations and Geometric Measure Theory
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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 04 Jun 2019



Inserted: 28 may 2019
Last Updated: 4 jun 2019

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


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