Blow-up analysis and existence results in the supercritical case for an asymmetric mean field equation with variable intensities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Jevnikar, Aleks¹ 

[1] Univ Roma Tor Vergata, Via Ric Sci 1, I-00133 Rome, Italy

关键词: Geometric PDEs;    Mean field equation;    Blow-up analysis;    Variational methods;   

DOI  :  10.1016/j.jde.2017.03.005

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free