## Differential and Integral Equations

### Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity

Amal Attouchi

#### Abstract

In this paper, we establish a local gradient estimate for a $p$-Laplacian equation with a fast growing gradient nonlinearity. This estimate allows us to prove a parabolic Liouville theorem for ancient solutions (i.e., defined for $t < 0$) satisfying some growth restriction near infinity.

#### Article information

Source
Differential Integral Equations Volume 29, Number 1/2 (2016), 137-150.

Dates
First available in Project Euclid: 24 November 2015

Attouchi, Amal. Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity. Differential Integral Equations 29 (2016), no. 1/2, 137--150. https://projecteuclid.org/euclid.die/1448323256.