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We are concerned with the mean field equation with singular data on boundeddomains. Under suitable non-degeneracy conditions we prove local uniqueness andnon-degeneracy of bubbling solutions blowing up at singular points. The proofis based on sharp estimates for bubbling solutions of singular mean fieldequations and suitably defined Pohozaev-type identities.

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