Abstract
An elliptic equation is considered in a domain \$D\_\varepsilon\$ that is obtained from a two-dimensional domain \$D\$ by removing a neighborhood of a segment. It is assumed that this neighborhood contracts to the segment as \$\varepsilon\to0\$. An asymptotic expansion of the solution of the first boundary value problem in \$D\_\varepsilon\$ is constructed and justified.
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