Some comments on a singular elliptic problem associated with a rectangle

SynopsisThe construction of the approximate solution within a rectangle of a singular elliptic problem is discussed. It is found that, provided the boundary data satisfy certain continuity conditions at the corners of the rectangle, ordinary boundary layers and parabolic boundary layers only are necessary to describe the solution. A correction term, however, has to be added to the solution if the continuity conditions on the boundary data are not satisfied.