Minicorso di Dottorato
LIOUVILLE EQUATIONS (MINICOURSE)
Andrea Malchiodi
10/05/2017 ore 09:00
fino al 15/05/2017
dove: Mercoledi' 10 Maggio ore 09-13 Aula 311
Giovedi' 11 Maggio ore 14-16 Aula 311, ore 16-18 Aula 211
Venerdi' 12 Maggio ore 09-11 Aula F, ore 11-13 Aula 009
Lunedi' 15 Maggio ore 09-13 Aula 311
We consider a class of Liouville equations and systems which arise in differential geometry when prescribing the Gaussian curvature of a surface, in models of mathematical physics describing stationary Euler flows and self-dual Chern-Simons equations or in spectral and string theory.
We discuss methods, variational in nature, to derive general existence results from suitable improvements of the Moser-Trudinger inequality combined with topological methods.
Tentative program:
1. Introduction and variational theory
2. Min-max construction
3. Singular Liouville equations
4. Toda systems
5. Liouville equations in spectral theory
