Advances in Differential Equations

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

Michel Chipot and Tetiana Savitska

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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

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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.

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