Geodesic
Characteristic Multipoles of Ellipse and a~Solution of the Electrostatic Problem for a~Conductive Ellipse in Applied Electric Fields
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 410-425.

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A method of the general problem of electrostatics solution for conductive ellipse in applied electric fields is obtained in complex form in terms of “characteristic multipole”. Both a general scheme of the solution and particular examples are considered. Complex Green functions for the outside and the inside of an ellipse are constructed. The terms “imaginary charge” and “ellipse of convergence” are established.
Keywords: complex Green function, characteristic multipole, conductive ellipse, ellipse of convergence, imaginary charge, electrostatic. 
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Vladimir P. Kazantsev; Evgeny N. Shlyahtich. Characteristic Multipoles of Ellipse and a~Solution of the Electrostatic Problem for a~Conductive Ellipse in Applied Electric Fields. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 4, pp. 410-425. http://geodesic.mathdoc.fr/item/JSFU_2009_2_4_a3/

[1] V. P. Kazantsev, Ponyatie o vysshikh polyarizuemostyakh uedinennykh provodnikov v ploskikh zadachakh elektrostatiki, Dep. v VINITI, 2291–V96, Krasnoyarsk, 1996

[2] V. P. Kazantsev, “Variatsionnye printsipy i vysshie polyarizuemosti uedinennykh provodnikov v ploskikh zadachakh elektrostatiki”, Dokl. RAN, 361:4 (1998), 469–473 | MR | Zbl

[3] V. P. Kazantsev, “Variatsionnye printsipy, elektricheskie kharakteristicheskie multipoli i vysshie polyarizuemosti v teorii polya”, Teoreticheskaya i matematicheskaya fizika, 119:3 (1999), 441–454 | Zbl