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

Daniele Bartolucci; Aleks Jevnikar; Youngae Lee; Wen Yang

doi:10.1016/j.jde.2020.01.030

paper

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

arXiv:1905.11749 · doi:10.1016/j.jde.2020.01.030

Abstract

We are concerned with the mean field equation with singular data on bounded domains. Under suitable non-degeneracy conditions we prove local 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.