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 estimates on the spatial derivatives of the associated diffusion semigroup which are of independent interest. In the proof we also use probabilistic techniques.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-2,
author = {Enrico Priola},
title = {Global Schauder estimates for a class of degenerate Kolmogorov equations},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {117-153},
zbl = {1178.35102},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-2}
}
Enrico Priola. Global Schauder estimates for a class of degenerate Kolmogorov equations. Studia Mathematica, Tome 192 (2009) pp. 117-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-2/