Inserted: 28 may 2019
Last Updated: 23 dec 2019
Journal: J. Diff. Eq.
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