Interior and boundary continuity of the solution of the singular equation $(beta(u))_t = Lu$

We extend some results of DiBenedetto and Vespri (Arch. Rational Mech. Anal 132(3) (1995) 247) proving the interior and boundary continuity of bounded solutions of the singular equation Image where Image is a second order elliptic operator with bounded measurable coefficients that depend both on space and time in a proper way.