Improved Moser-Trudinger inequalities and Liouville equations on compact surfaces

Improved Moser-Trudinger inequalities and Liouville equations on compact surfaces

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Andrea Malchiodi, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste
Fine Hall 314

We consider a class of equations with exponential nonlinearities and possibly singular sources motivated from the study of abelian Chern Simons models or from the problem of prescribing a metric with conical singularities through conformal transformations. Using new improvements of the classical Moser-Trudinger inequality and, combined with topological methods, we derive some general existence results.