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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