Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola. "Global Schauder estimates for a class of degenerate Kolmogorov equations." Studia Mathematica 194.2 (2009): 117-153. <http://eudml.org/doc/284768>.

@article{EnricoPriola2009,
abstract = {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 $L^\{∞\}-C^\{θ\}$ estimates on the spatial derivatives of the associated diffusion semigroup which are of independent interest. In the proof we also use probabilistic techniques.},
author = {Enrico Priola},
journal = {Studia Mathematica},
keywords = {diffusion semigroups; Ornstein-Uhlenbeck type operators; unbounded coefficients; probabilistic techniques},
language = {eng},
number = {2},
pages = {117-153},
title = {Global Schauder estimates for a class of degenerate Kolmogorov equations},
url = {http://eudml.org/doc/284768},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Enrico Priola
TI - Global Schauder estimates for a class of degenerate Kolmogorov equations
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 2
SP - 117
EP - 153
AB - 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 $L^{∞}-C^{θ}$ estimates on the spatial derivatives of the associated diffusion semigroup which are of independent interest. In the proof we also use probabilistic techniques.
LA - eng
KW - diffusion semigroups; Ornstein-Uhlenbeck type operators; unbounded coefficients; probabilistic techniques
UR - http://eudml.org/doc/284768
ER -