### 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.

#### Article information

Source
Adv. Differential Equations Volume 8, Number 11 (2003), 1341-1376.

Dates
First available in Project Euclid: 19 December 2012

Mathematical Reviews number (MathSciNet)
MR2016650

Zentralblatt MATH identifier
1112.35039

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35B65: Smoothness and regularity of solutions 35D10

#### Citation

Gianazza, Ugo; Vespri, Vincenzo. Continuity of weak solutions of a singular parabolic equation. Adv. Differential Equations 8 (2003), no. 11, 1341--1376. https://projecteuclid.org/euclid.ade/1355926120.