Accepted Paper

Inserted: 15 sep 2016
Last Updated: 6 mar 2017

Journal: J. Diff. Eq.
Year: 2017

Abstract:

A class of equations with exponential nonlinearities on a compact Riemannian surface is considered. More precisely, we study an asymmetric sinh-Gordon problem arising as a mean field equation of the equilibrium turbulence of vortices with variable intensities.

We start by performing a blow-up analysis in order to derive some information on the local blow-up masses. As a consequence we get a compactness property in a supercritical range.

We next introduce a variational argument based on improved Moser-Trudinger inequalities which yields existence of solutions for any choice of the underlying surface.

Keywords: Variational methods, blow-up analysis, Geometric PDEs, Mean field equation

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• Liouv-prob.pdf