Global Schauder estimates for a class of degenerate Kolmogorov equations

• Autorzy: Enrico Priola
• Języki publikacji: EN

Abstrakty

EN

We consider a class of possibly degenerate second order elliptic operators 𝓐 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 𝓐. The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator 𝓐. 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.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 47D07: Markov semigroups and applications to diffusion processes
• 35J70: Degenerate elliptic equations
• 35B65: Smoothness and regularity of solutions
• 35K65: Degenerate parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 2
• Strony: 117-153

Daty

wydano

2009

Twórcy

autor

Enrico Priola

• Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Identyfikatory

DOI

10.4064/sm194-2-2