Wiener-Landis criterion for Kolmogorov-type operators

TL;DR

This paper develops a new criterion for boundary regularity in Kolmogorov-type equations, extending classical heat equation criteria to a broader class of differential operators.

Contribution

It introduces a Wiener-Landis type criterion that provides necessary and sufficient conditions for boundary regularity in Kolmogorov-type operators.

Findings

Established a Wiener-Landis criterion for Kolmogorov operators

Connected classical heat equation criteria to Kolmogorov-type equations

Provided a complete characterization of boundary regularity

Abstract

We establish a necessary and sufficient condition for a boundary point to be regular for the Dirichlet problem related to a class of Kolmogorov-type equations. Our criterion is inspired by two classical criteria for the heat equation: the Evans-Gariepy's Wiener test, and a criterion by Landis expressed in terms of a series of caloric potentials.