Geodesic
A method of Fourier series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen)
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1209-1213

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In the framework of the theory of harmonic functions, potentials of steady state processes (heat conduction, filtration, or electrostatics) in the piecewise inhomogeneous plane separated by a rectilinear strongly permeable crack or by a weakly permeable screen into two half-planes with quadratic permeability functions are constructed. The motion is induced by given singular points of the potential (sources, sinks, etc.). Compact formulas that directly express potentials in these domains in terms of harmonic functions are obtained; the resulting functions map the set of harmonic functions to the set of potentials conserving the type of singularities. 
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     author = {S. E. Kholodovskii},
     title = {A~method of {Fourier} series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen)},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1209--1213},
     publisher = {mathdoc},
     volume = {48},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a6/}
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S. E. Kholodovskii. A method of Fourier series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen). Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1209-1213. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a6/