Geodesic
Solution of boundary value problems in cylinders separated by a three-layer film into two semicylinders
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1261-1266 
N. V. Nutchina-Pestryakova; S. E. Kholodovskii. Solution of boundary value problems in cylinders separated by a three-layer film into two semicylinders. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1261-1266. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a7/
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     title = {Solution of boundary value problems in cylinders separated by a three-layer film into two semicylinders},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Boundary value problems are considered for the class of equations $\partial_x^2u+L[u]=0$ in cylinders $D=(x\in R,\,y\in Q\subseteq R^m)$ with an infinitely thin film at $x=0$ consisting of three sublayers with alternating high and low permeability ($L$-linear differential operator with respect to $y_i$). The solutions of the problems are expressed in terms of those of the corresponding classical boundary value problems in homogeneous cylinders $D$ with no film. The resulting formulas have the form of simple quadrature rules, which are amenable to numerical computations.

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