Uniqueness of solutions of mean field equations in 𝑅²

Gui, Changfeng; Moradifam, Amir

doi:10.1090/proc/13814

Uniqueness of solutions of mean field equations in $R^2$
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by Changfeng Gui and Amir Moradifam PDF

Proc. Amer. Math. Soc. 146 (2018), 1231-1242 Request permission

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.

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