New Improved Moser–Trudinger Inequalities and Singular Liouville Equations on Compact Surfaces


DOI: 10.1007/s00039-011-0134-7

Cite this article as:
Malchiodi, A. & Ruiz, D. Geom. Funct. Anal. (2011) 21: 1196. doi:10.1007/s00039-011-0134-7


We consider a singular Liouville equation on a compact surface, arising from the study of Chern–Simons vortices in a self-dual regime. Using new improved versions of the Moser–Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.

Keywords and phrases

Geometric PDEs variational methods min-max schemes 

2010 Mathematics Subject Classification

35J20 35R01 53A30 

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Sector of Mathematical AnalysisSISSATriesteItaly
  2. 2.Departamento de Análisis MatemáticoUniversity of GranadaGranadaSpain

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