Asymptotic expansions of solutions to Dirichlet problem for elliptic equation with singularities

Abstract

The paper proposes an analogue of Vishik–Lyusternik–Vasileva–Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to bisingular perturbed problems. By means of this method we construct the uniform asymptotic expansion for the solution to the Dirichlet problem for bisingular perturbed second order elliptic equation with two independent variables in a circle. By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established.