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BIRS Workshop Lecture Videos

Liouville problems with sign changing potentials López Soriano, Rafael


This talk is concerned with the singular mean field problem of Liouville type on compact surfaces. The study of this equation is motivated by some problems which arise in Differential Geometry and Physics. We will focus on the existence and compactness of solutions, which have been extensively studied for positive potentials. However, the case of sign changing potentials has not been much considered in the literature. For the latter case, we present results on the solvability using variational techniques. Concerning the compactness, we deal with the possible blow--up phenomena in order to establish a general criterion. Joint works with Francesca De Marchis and David Ruiz.

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