# Intrinsic $C^1$ and Lipschitz graphs in the Heisenberg group and continuous solutions of Burgers' equation

## Francesco Serra Cassano

### (Dip. Mat. Univ. Trento)

Date: Oct 11, 2011, time: 09:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. We are going to discuss on a characterization of di erent (weak) continuous solutions of Burgers' equation and functions which induce intrinsic $C^1$ and Lipschitz graphs in the rst Heisenberg group $H^1 \equiv R^3$, endowed with its standard Sub-Riemanniam metric structure, named also of Carnot-Carathéodory . We will also extend the characterization to higher Heisenberg groups $H^n \equiv R^{2n+1}$.