Regularity results for Kolmogorov equations based on a blow-up argument

Abstract

We present recent results regarding the regularity theory for degenerate second order differential operators of Kolmogorov-type. In particular, we focus on Schauder estimates for classical solutions to Kolmogorov equations in non-divergence form with Dini-continuous coefficients obtained in [30] in collaboration with S. Polidoro and B. Stroffolini. Furthermore, we discuss new pointwise regularity results and a Taylor-type expansion up to second order with estimate of the rest in Lp norm, following the recent paper [14] in collaboration with E. Ipocoana. The proofs of both results are based on a blow-up technique.

Keywords

• degenerate kolmogorov equations
• regularity theory
• classical solutions
• dini continuity
• taylor formula
• pointwise regularity
• bmo pointwise estimate
• vmo pointwise estimate