Regularity of a boundary point for singular parabolic equations with measurable coefficients

Abstract

We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equations considered is the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the Laplace p-operator Δ p for 2n/ (n + 1) < p < 2.