CodiceQDD 67
TitoloBasic properties of nonsmooth Hormander s vector fields and Poincare s inequality
Autore/iBramanti, M.; Brandolini, L.; Pedroni, M.
LinkDownload full text
AbstractWe consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander s rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander s vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow s connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare s inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander s vector fields.