We consider some singular Liouville equations and systems motivated by uniformization problems in a non-smooth setting, as well as from models in mathematical physics. We will study the existence of solutions from a variational point of view, using suitable improvements of the Moser-Trudinger inequality. These reduce the problem to a topological one by studying the concentration property of conformal volume, which will be constrained by the functional inequalities of geometric flavour. We will mainly describe some common strategies from the papers [11, 12, 20] in simple situations to give an idea to the non-expert reader about the general methods we use.

On singular Liouville equations and systems

MALCHIODI, ANDREA
2017

Abstract

We consider some singular Liouville equations and systems motivated by uniformization problems in a non-smooth setting, as well as from models in mathematical physics. We will study the existence of solutions from a variational point of view, using suitable improvements of the Moser-Trudinger inequality. These reduce the problem to a topological one by studying the concentration property of conformal volume, which will be constrained by the functional inequalities of geometric flavour. We will mainly describe some common strategies from the papers [11, 12, 20] in simple situations to give an idea to the non-expert reader about the general methods we use.
2017
Settore MAT/05 - Analisi Matematica
Geometric PDEs; Min-Max Schemes; Singular Liouville Equation; Variational Methods;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/64423
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