Geodesic
A~boundary value problem for the elliptic equation of second order in a~domain with a~narrow slit. 1.~The two-dimensional case
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 459-480

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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. Bibliography: 5 titles. 
@article{SM_1976_28_4_a1,
     author = {A. M. Il'in},
     title = {A~boundary value problem for the elliptic equation of second order in a~domain with a~narrow slit. {1.~The} two-dimensional case},
     journal = {Sbornik. Mathematics},
     pages = {459--480},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_4_a1/}
}
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A. M. Il'in. A~boundary value problem for the elliptic equation of second order in a~domain with a~narrow slit. 1.~The two-dimensional case. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 459-480. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a1/