On a degenerate elliptic singular perturbation

Abstract

The method of constructive reduction of elliptic and coercive singular perturbations to regular ones, developed in [2–7] is applied to so-called bisingular singularly perturbed boundary value problems (see, for instance, [8]). The reduction procedure allows to derive asymptotic formulae for the solutions of these problems, without going through the matching of different locally formally derived asymptotic expansions (see [8,9,11]). The advantage of using the reduction procedure consists not only in the globality of asymptotic formulae thus obtained, but also in a simple proof of their asymptotic convergence as a direct consequence of the central reduction to regular perturbations result.