×

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 \(\omega\).

MSC:

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)
PDFBibTeX XMLCite