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

## TL;DR

This paper proves local uniqueness and non-degeneracy of bubbling solutions in singular mean field equations on bounded domains, using sharp estimates and Pohozaev identities.

## Contribution

It establishes the conditions for local uniqueness and non-degeneracy of blow-up solutions in singular mean field equations, advancing understanding of their behavior.

## Key findings

- Proved local uniqueness of bubbling solutions.
- Established non-degeneracy under certain conditions.
- Developed sharp estimates and Pohozaev identities for analysis.

## 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.