On the Dirichlet Boundary Value Problem for a Degenerate Parabolic Equation
Tero Kilpeläinen, Peter Lindqvist · SIAM Journal on Mathematical Analysis · 1996
The Perron method for degenerate parabolic equations like $u_t = {\operatorname{div}}(| abla u|^{p - 2} abla u)$ 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.