New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

Details New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

2010-07-22

arxiv.org/abs/1007.3861v2

Mathematics

Analysis of PDEs

to appear in GAFA

Scientific paper

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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