Continuity of weak solutions of a singular parabolic equation

Abstract

We prove the continuity of bounded, weak solutions of the singular parabolic equation $ \beta(u)_t=Lu, $ where $Lu$ is a second-order, uniformly elliptic operator in divergence form with bounded and measurable coefficients and $\beta(\cdot)$ is a maximal monotone graph in ${\bf R}\times {\bf R}$ exhibiting an arbitrary but finite number of jumps.