A detour on Sobolev type inequalities in the Heisenberg group
and applications to critical subelliptic problems

Profª. Patrizia Pucci
Università degli Studi di Perugia

Abstract: Motivated by important applications to geometric control theory and PDEs, great attention has been recently devoted to the study of geometric inequalities in the context of stratified Lie groups.

In the first part of the talk we present some classical results and open problems related to the Sobolev type inequalities in the Heisenberg group. In the second part, we apply these inequalities to obtain existence results for nonlinear problems involving subelliptic operators of Marcellini's type in the Heisenberg group.