Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders
type: Item
instance of: scholarly article
title: Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders
zbMATH Open document ID: 1158.35042
published in: Advances in Differential Equations
publication date: 2008-09-12T00:00:00Z
review text: The author considers the behavior of a nonlinear monotone elliptic boundary value problem in a cylinder \((l,l)^q \times \omega\), with a source term in \(L^1(\omega) + W^{1,p'}(\omega)\) (\(p\) is the growth exponent in the coefficients of the operator and \(p'\) is the dual exponent for \(p\)) and homogeneous Cauchy-Dirichet boundary conditions. Under suitable assumptions on the dependence of the coefficients on variables \(x_1, x_2\) and assuming that the source term depends only on \(x_2\), the author shows that the solutions \(u_l\) converge, in a suitable sense, as \(l\rightarrow 0\) to the solution of the same problem in \(\omega\).
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 5343680
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonlinear monotone elliptic problem
zbMATH Keywords: regularity
zbMATH Keywords: boundary value problems
author: Nicolas Bruyère
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5343680