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Uniqueness of solutions of mean field equations in $ R^2$

Authors: Changfeng Gui and Amir Moradifam
Journal: Proc. Amer. Math. Soc. 146 (2018), 1231-1242
MSC (2010): Primary 35B30, 35J60, 35A23, 35J91; Secondary 35B10, 35J99
Published electronically: December 7, 2017
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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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Additional Information

Changfeng Gui
Affiliation: Department of Mathematics, University of Texas at San Antonio, San Antonio, Texas 78249

Amir Moradifam
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

Received by editor(s): December 26, 2016
Received by editor(s) in revised form: May 4, 2017, and May 8, 2017
Published electronically: December 7, 2017
Additional Notes: The first author was partially supported by a Simons Foundation Collaborative Grant (Award No 199305), NSFC grant No 11371128, and NSF grant DMS-1601885.
The second author is partially supported by NSF grant DMS-1715850.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society

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