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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Abstract

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

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

Dates
First available in Project Euclid: 18 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1408367286

Mathematical Reviews number (MathSciNet)
MR3250760

Zentralblatt MATH identifier
1307.35151

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

Citation

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. https://projecteuclid.org/euclid.ade/1408367286.


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