Limit behaviour of a class of nonlinear elliptic problems in infinite cylinders
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 \(\omega\).
scientific article; zbMATH DE number 5343680