Uniqueness of solutions of mean field equations in ${\mathbb{R}}^2$

Abstract

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.

arXiv commentto appear in Proceedings of the AMS

References in corpus (1)

• On the Best Constant in the Moser-Onofri-Aubin Inequality

Cited by in corpus (3)

• The sphere covering inequality and its dual
• Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains
• Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass