Abstract: A boundary point with respect to a given equation is called regular if all solutions to the Dirichlet problem attain their boundary values continuously at that point. The characterization of regular boundary points has a long history including various Wiener and Petrovskiĭ type criteria for different equations. In this talk, I will examine how we can characterize regular boundary points using a barrier family condition for a non-divergence form equation generalizing both the usual p-parabolic equation and the normalized equation arising from stochastic game theory. I will also show that for the singular case, the existence of a single barrier function is not enough to guarantee regularity.
