Advances in Differential Equations

Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient

Michel Chipot and Tetiana Savitska

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We are studying a class of nonlinear nonlocal diffusion problems associated with a p-Laplace-type operator, where a nonlocal quantity is present in the diffusion coefficient. We address the issues of existence and uniqueness for the parabolic setting. Then, we study the asymptotic behavior of the solution for large time. For this purpose, we introduce and investigate, in detail, the associated stationary problem. Moreover, since the solutions of the stationary problem are also critical points of some energy functional, we make a classification of its critical points.

Article information

Adv. Differential Equations, Volume 19, Number 11/12 (2014), 997-1020.

First available in Project Euclid: 18 August 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35K55: Nonlinear parabolic equations 35K92: Quasilinear parabolic equations with p-Laplacian 37B25: Lyapunov functions and stability; attractors, repellers


Chipot, Michel; Savitska, Tetiana. Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient. Adv. Differential Equations 19 (2014), no. 11/12, 997--1020.

Export citation