Uniqueness of solutions of mean field equations in $\R^2$
  In this paper, we prove uniqueness of solutions of mean field equations with general boundary conditions for the critical and subcritical total mass regime, extending the earlier results for null Dirichlet boundary condition. The proof is based on new Bol's inequalities for weak radial solutions obtained from rearrangement of the solutions. 
Changfeng Gui and Amir Moradifam
math.AP