Calculus of Variations and Geometric Measure Theory

C. Gui - A. Jevnikar - A. Moradifam

Symmetry and uniqueness of solutions to some Liouville-type equations and systems

created by jevnikar on 10 Jan 2017
modified on 19 Nov 2017


Comm. PDEs

Inserted: 10 jan 2017
Last Updated: 19 nov 2017

Year: 2017


We are concerned with symmetry and uniqueness results for three classes of Liouville-type problems defined on bounded domains arising in geometry and mathematical physics: asymmetric Sinh-Gordon equation, cosmic string equation and Toda system. In the spirit of the Sphere covering inequality we provide a series of results under suitable assumptions on the mass associated to these problems.

Keywords: uniqueness results, Geometric PDEs, Sinh-Gordon equation, Toda system, Cosmic string equation, Sphere covering inequality, Symmetry results