PDE Seminar Abstracts

In this talk we will consider a Liouville equation on a compact surface. This problem appears in physical models like the abelian Chern-Simons-Higgs theory and the Electroweak theory. Moreover, it is also related to the problem of prescribing the Gaussian curvature of a surface via a conformal deformation of the metric. If the surface has some conical points, Dirac deltas appear in the equation; this is the case we are interested in.

Our techniques are variational, that is, we look for solutions as critical points of an associated energy functional. In order to do that, the study of the topology of the sublevels of that functional becomes very important. This is accomplished thanks to a convenient Moser-Trudinger type inequality.

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