Calculus of Variations and Geometric Measure Theory

A variational approach to Liouville equations

Andrea Malchiodi (Scuola Normale Superiore)

created by ambrosio on 13 Jul 2014

18 jul 2014 -- 10:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi


We consider Liouville equations with variational structure arising from curvature prescription problems and from models in Electroweak or Chern-Simons theory. We show how improved versions of the Moser-Trudinger inequality may reduce these PDEs to the study of finite-dimensional topological spaces. We then derive existence of solutions via min-max or Morse theory.