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November/December 2014 Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient
Michel Chipot, Tetiana Savitska
Adv. Differential Equations 19(11/12): 997-1020 (November/December 2014).

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.

Citation

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Michel Chipot. Tetiana Savitska. "Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient." Adv. Differential Equations 19 (11/12) 997 - 1020, November/December 2014.

Information

Published: November/December 2014
First available in Project Euclid: 18 August 2014

zbMATH: 1307.35151
MathSciNet: MR3250760

Subjects:
Primary: 35J60, 35K55, 35K92, 37B25

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 11/12 • November/December 2014
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