Geodesic
$\mathbb R$-linear conjugation problem for a confocal parabolic annulus
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 170-178

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The article presents an analytical closed-form solution derived for an $\mathbb R$-linear conjugation problem for a confocal parabolic annulus. The cases of real and complex coefficients of boundary conditions are comprehensively studied. The solution is found in the class of piece-wise holomorphic functions with fixed finite value at infinity in one of the media components.
Keywords: heterogeneous media, $\mathbb R$-linear conjugation problem, holomorphic functions. 
@article{UZKU_2009_151_3_a14,
     author = {Yu. V. Obnosov and M. A. Egorova},
     title = {$\mathbb R$-linear conjugation problem for a~confocal parabolic annulus},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {170--178},
     publisher = {mathdoc},
     volume = {151},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a14/}
}
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Yu. V. Obnosov; M. A. Egorova. $\mathbb R$-linear conjugation problem for a confocal parabolic annulus. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 170-178. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a14/