A BOUNDARY VALUE PROBLEM FOR THE ELLIPTIC EQUATION OF SECOND ORDER IN A DOMAIN WITH A NARROW SLIT. 1. THE TWO-DIMENSIONAL CASE
Арлен Михайлович Ильин · Mathematics of the USSR-Sbornik · 1976
An elliptic equation is considered in a domain that is obtained from a two-dimensional domain by removing a neighborhood of a segment. It is assumed that this neighborhood contracts to the segment as . An asymptotic expansion of the solution of the first boundary value problem in is constructed and justified. Bibliography: 5 titles.