Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients

Abstract

We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation $\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0$ with the p-Laplace operator Δp. We prove a sufficient condition for the regularity of a boundary point in terms of C _p-capacity.