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

Amal Attouchi (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near infinity.

Mots clés: p-Laplacian; local gradient estimate; parabolic Liouville-type Theorem; gradient non-linearity

Domaines: Equations aux dérivées partielles [math.AP]

Amal Attouchi. Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity. 2014. ⟨hal-00994918⟩