Codice  QDD 67 
Titolo  Basic properties of nonsmooth Hormander s vector fields and Poincare s inequality 
Data  20101021 
Autore/i  Bramanti, M.; Brandolini, L.; Pedroni, M. 
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Abstract  We 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 r1 continuous derivatives. We extend to this nonsmooth context some results which are wellknown 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^{r1,1}, 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. 
