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2007 Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders
Nicolas Bruyère
Adv. Differential Equations 12(10): 1081-1114 (2007).

Abstract

We study the asymptotic behaviour of the solution of nonlinear monotone elliptic problem \begin{equation*} -{\operatorname{div}}[a(x,Du_l)] = \mu \mbox{ on } \ ( -l,l)^q \times {\omega} \end{equation*} with homogeneous Cauchy-Dirichlet boundary conditions, where ${\omega}$ is a bounded, open, connected subset of $\mathbb R^{N-q}$ with second member in $L^{1}{\omega} +W^{-1,p'}(\omega)$, using the framework of renormalized solutions. Assuming specific dependence of the operator $a$ with respect to the variable $(x_1,x_2) \in ( -l,l ) ^q \times {\omega}$ and that $\mu=\mu(x_2)$, we show the convergence of $u_l$, in an appropriate sense, toward the solution of the same problem posed in $\omega$.

Citation

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Nicolas Bruyère. "Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders." Adv. Differential Equations 12 (10) 1081 - 1114, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1158.35042
MathSciNet: MR2362264

Subjects:
Primary: 35J60
Secondary: 35B40, 35D10, 35J25

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.12 • No. 10 • 2007
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