Global Schauder estimates for a class of degenerate Kolmogorov equations
Abstract
Description
We consider a class of possibly degenerate second order elliptic operators $\cal
A$ on $\R^n$. 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 ${\cal A}$. The Hölder function spaces are defined with respect to a non-euclidean metric related to the operator $\cal A$.