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


  • Annalaura Rebucci Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany.



Degenerate Kolmogorov equations, Regularity theory, Classical solutions, Dini continuity, Taylor formula, Pointwise regularity, BMO pointwise estimate, VMO pointwise estimate


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.




How to Cite

Rebucci, A. (2024). Regularity results for Kolmogorov equations based on a blow-up argument. Bruno Pini Mathematical Analysis Seminar, 14(2), 139–162.