We consider a class of Liouville equations motivated by uniformization problems in a singular setting, as well as from models in Mathematical Physics. We will study existence from a variational point of view, using suitable improvements of the Moser-Trudinger inequality. These improvements allow to study the concentration properties of conformal volume, and to reduce the problem to studying explicit finite-dimensional objects.

A Variational approach to Liouville Equations

MALCHIODI, ANDREA
2017

Abstract

We consider a class of Liouville equations motivated by uniformization problems in a singular setting, as well as from models in Mathematical Physics. We will study existence from a variational point of view, using suitable improvements of the Moser-Trudinger inequality. These improvements allow to study the concentration properties of conformal volume, and to reduce the problem to studying explicit finite-dimensional objects.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/64422
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