Differential and Integral Equations

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

Amal Attouchi

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1448323256

Mathematical Reviews number (MathSciNet)
MR3450752

Zentralblatt MATH identifier
1349.35215

Subjects
Primary: 35K65: Degenerate parabolic equations 35K92: Quasilinear parabolic equations with p-Laplacian 35B45: A priori estimates 35B53: Liouville theorems, Phragmén-Lindelöf theorems 35K55: Nonlinear parabolic equations

Citation

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.


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