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

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Abstract

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.

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Authors and Affiliations

  1. Sector of Mathematical Analysis, SISSA, via Bonomea 265, 34136, Trieste, Italy

    Andrea Malchiodi

  2. Departamento de Análisis Matemático, University of Granada, 18071, Granada, Spain

    David Ruiz

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  1. Andrea Malchiodi
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  2. David Ruiz
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Correspondence to Andrea Malchiodi.

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Malchiodi, A., Ruiz, D. New Improved Moser–Trudinger Inequalities and Singular Liouville Equations on Compact Surfaces. Geom. Funct. Anal. 21, 1196–1217 (2011). https://doi.org/10.1007/s00039-011-0134-7

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