Geodesic
Skin-phenomenon in the case of a~wire with arbitrary cross-section
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 13-20

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An asymptotic theory of skin-phenomenon is developed. The important part of construction is matching of asymptotic expansions. The problem is reduced to solution of a sequence of Dirichlet problems for the domain $\mathbb R^2\setminus\Omega$ ($\Omega$ is the cross section of the wire). 
@article{ZNSL_1983_128_a1,
     author = {V. M. Babich},
     title = {Skin-phenomenon in the case of a~wire with arbitrary cross-section},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--20},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a1/}
}
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V. M. Babich. Skin-phenomenon in the case of a~wire with arbitrary cross-section. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 13-20. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a1/