9/16/2011

Andrea Malchiodi
SISSA, Trieste

Improved Moser-Trudinger inequalities and Liouville equations on compact surfaces

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.