On the Dirichlet Problem for hypoelliptic evolution equations:   Perron-Wiener solution and a cone-type criterion
  We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan. 
Alessia E. Kogoj
math.AP