## Differential and Integral Equations

### Lower semicontinuity of weak supersolutions to nonlinear parabolic equations

Tuomo Kuusi

#### Abstract

We prove that weak supersolutions to equations similar to the evolutionary $p$-Laplace equation have lower semicontinuous representatives. The proof avoids the use of Harnack's inequality and, in particular, the use of parabolic BMO. Moreover, the result gives a new point of view to approaching the continuity of the solutions to a second-order partial differential equation in divergence form.

#### Article information

Source
Differential Integral Equations Volume 22, Number 11/12 (2009), 1211-1222.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019413

Mathematical Reviews number (MathSciNet)
MR2555645

Zentralblatt MATH identifier
1240.35220

Subjects
Primary: 35K92: Quasilinear parabolic equations with p-Laplacian
Secondary: 35B51: Comparison principles

#### Citation

Kuusi, Tuomo. Lower semicontinuity of weak supersolutions to nonlinear parabolic equations. Differential Integral Equations 22 (2009), no. 11/12, 1211--1222.https://projecteuclid.org/euclid.die/1356019413