Asymptotics of the Solution to the Boundary-Value Problems with Non Smooth Coefficient

Abstract

The first boundary-value problem for a linear inhomogeneous second-order partial differential equation of elliptic type with two independent variables in a ring is investigated in the case when the potential is a non smooth function. Using the modified method of boundary functions, a uniform asymptotic expansion of the solution of the Dirichlet problem is constructed. The maximum principle is used to obtain an estimate for the remainder term of the asymptotic expansion. The resulting series is asymptotic in the sense of Erdey.