We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

We study, with purely analytic tools, existence, uniqueness and gradient estimates of the solutions to the Neumann problems associated with a second order elliptic operator with unbounded coefficients in spaces of continuous functions in an unbounded open set Ω in ${ℝ}^N$.