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Let be a family of vector fields in , where are locally Lipschitz continuous functions in . As usual, we identify the vector field Xj with the first order differential operator In this article we c...

(2000). Non-existence results for semilinear kohn-laplace equations in unbounded domains. Communications in Partial Differential Equations: Vol. 25, No. 9-10, pp. 1703-1739.

In the first part of this paper we study some differentiabilityperties properties (In Sobolev space setting)of functions belonging to thespace generated by the vector fields in aJ J Dx.connected open subset of Rn ; here the λjs are continuous (but in generalnot smooth) and nonnegative. In particular, under suitable geometricalhypotheses involving the integral curves of we get thenfollowing embedding estimate: for all test functions u and for suitable positive constants e and CP depending only on the "order of degeneration" of the vector fields Such a problem arises naturally in study of the pointewise estimates for the weak solutions of some degenerate elliptic equations with measurable coefficients.