On the Dirichlet Boundary Value Problem for a Degenerate Parabolic Equation

The Perron method for degenerate parabolic equations like $u_t = {\operatorname{div}}(|\nabla u|^{p - 2} \nabla u)$ is studied. The regular boundary points for the Dirichlet problem are characterized in terms of barriers. In the particular case of the space-time cylinder $G \times (0,T)$ , a geometric characterization in terms of a Wiener-type test is given for regularity.