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On the asymptotic behaviour of the p-Laplace equation in cylinders becoming unbounded


Chipot, M; Xie, Y (2004). On the asymptotic behaviour of the p-Laplace equation in cylinders becoming unbounded. In: Kenmochi, N; Ôtani, M; Zheng, S. Nonlinear partial differential equations and their applications. Tokyo: Gakko Tosho, 16-27.

Abstract

In the rectangle Ωℓ = (−ℓ, ℓ) × (−1, 1), we consider the weak solution uℓ to the p-Laplace equation for a right hand side depending on x2 only. We show that, for any ℓ0 > 0, uℓ → u∞ in W 1,p(Ωℓ 0 ) when ℓ → ∞, where u∞ is the solution of the p-Laplace equation on the section.

Abstract

In the rectangle Ωℓ = (−ℓ, ℓ) × (−1, 1), we consider the weak solution uℓ to the p-Laplace equation for a right hand side depending on x2 only. We show that, for any ℓ0 > 0, uℓ → u∞ in W 1,p(Ωℓ 0 ) when ℓ → ∞, where u∞ is the solution of the p-Laplace equation on the section.

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Additional indexing

Other titles:Proceedings of the international conference on nonlinear partial differential equations and their applications, Shanghai, China, November 23–27, 2003.
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:p-Laplace equation, W 1,p and L ∞ convergence, asymptotic behaviour
Language:English
Date:2004
Deposited On:16 Dec 2009 13:04
Last Modified:19 Feb 2018 20:33
Publisher:Gakko Tosho
Series Name:GAKUTO International Series. Mathematical Sciences and Applications.
Number:20
ISBN:4-7625-0429-7
OA Status:Green
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1080.35022

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