The corner boundary layer in nonlinear singularly perturbed elliptic equations. (Q1395325)

In this paper the author analyzes the possibility of constructing an asymptotic expansion of the solution to the Dirichlet problem for the elliptic equation \({\varepsilon}^2{\Delta}u=F(u,x,y,\epsilon)\) defined on a rectangle. As compared to previous studies, the analysis is performed without two restrictions, which means that it applies to arbitrary nonlinear functions \(F(u,x,y,\varepsilon)\). The main result consist in the construction of the corner part of an asymptotic solution to the boundary value problem.