REGULARITY RESULTS FOR KOLMOGOROV EQUATIONS BASED ON A BLOW-UP ARGUMENT

We present recent results regarding the regularity theory for degenerate sec-ond 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.