Calculus of Variations and Geometric Measure Theory

P. Bousquet - L. Brasco - C. Leone - A. Verde

Gradient estimates for an orthotropic nonlinear diffusion equation

created by brasco on 01 May 2021
modified on 01 Dec 2021


Accepted Paper

Inserted: 1 may 2021
Last Updated: 1 dec 2021

Journal: Adv. Calc. Var.
Pages: 29
Year: 2021

Shortly after the completion of this paper, we sadly learned about the passing of Emmanuele DiBenedetto. We wish to humbly dedicate this paper to his memory, with esteem, admiration and gratitude. This is a small token of appreciation for his groundbreaking contributions in the field of Regularity Theory.


We consider a quasilinear degenerate parabolic equation driven by the orthotropic $p-$Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time.

Keywords: lipschitz continuity, Degenerate parabolic equations, anisotropic operators