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

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 with the Laplace p-operator _p for 2n / (n + 1) < p < 2.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 506–516, April, 2004.