Geometric and Functional Analysis

, 21:1196

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


    • Sector of Mathematical AnalysisSISSA
  • David Ruiz
    • Departamento de Análisis MatemáticoUniversity of Granada

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 PDEsvariational methodsmin-max schemes

2010 Mathematics Subject Classification

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© Springer Basel AG 2011