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May  2018, 38(5): 2467-2485. doi: 10.3934/dcds.2018102

## Wiener-Landis criterion for Kolmogorov-type operators

 1 Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino "Carlo Bo", Piazza della Repubblica, 13 - 61029 Urbino (PU), Italy 2 Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta San Donato, 5 - 40126 Bologna, Italy 3 Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5 - 00185 Roma, Italy

* Corresponding author: Alessia E. Kogoj

Received  February 2017 Revised  November 2017 Published  March 2018

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.

Citation: Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli. Wiener-Landis criterion for Kolmogorov-type operators. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2467-2485. doi: 10.3934/dcds.2018102
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