Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders. (English) Zbl 1158.35042

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 \(\omega\).


35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)