A singularly-perturbed, elliptic boundary value problem is considered in a square. A theory of corner singularities for a 90^ ∘ angle that takes account of lower-order terms in the equation is developed. In the case r(x,y) ≡ const., an asymptotic expansion of the solution is obtained that can be differentiated termwise and which displays both the corner singularities and the boundary and corner layers of the solution.
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Han et al. (1990) studied this question.