Disuguaglianze di Harnack alla frontiera per equazioni di Kolmogorov

Abstract

We describe some recent results on the boundary regularity for hypoelliptic Kolmogorov equations. We prove boundary Harnack inequalities of the positive solutions to Kolmogorov equations vanishing on some relatively open subset of the boundary. Sufficient conditions for the boundary Harnack inequality are given in terms of cone conditions, that are satisfied by a wide class of Lipschitz domains. We also prove Carleson type estimates, that are scale-invariant and generalize previous results valid for second order uniformly parabolic equations.