Literature Cited
Ya. S. Soibel'man, “An analytic formula for condenser capacity,” Dokl. Akad. Nauk SSSR,258, No. 3, 590–593 (1981).
G. Kirchhoff, “Zur Theorie des Kondensators,” Monatsb. Deutsch Akad. Wiss. Berlin, 101–120 (1877).
V. S. Ignatovskii, “Circular plate condenser,” Tr. Mosk. Inst. Akad. Nauk SSSR,2, No. 3, 1–104 (1932).
G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton Univ. Press (1951).
V. Hutson, “The circular plate condenser at small separations,” Proc. Cambridge Philos. Soc.,59, No. 3, 211–224 (1963).
F. Leppington and H. Levine, “On the capacity of the circular disk condenser at small separation,” Proc. Cambridge Philos. Soc.,68, No. 4, 235–254 (1970).
S. J. N. Shaw, “Circular-disk viscometer and related electrostatic problems,” Phys. Fluids,13, No. 8, 1935–1947 (1970).
L. A. Wigglesworth, “Comments on ‘Circular disk viscometer and related electrostatic problems,’” Phys. Fluids,15, No. 4, 718–719 (1972).
W. C. Chew and J. A. Kong, “Asymptotic formula for the capacitance of two oppositely charged disks,” Math. Proc. Cambridge Philos. Soc.,89, No. 3, 373–384 (1981).
M. Van Dyke, Asymptotic Methods in Fluid Mechanics [Russian translation], Nauka, Moscow (1964).
V. A. Kondrat'ev, “Boundary-value problems for elliptic equations in domains with conical or angular points,” Tr. Mosk Mat. Obshch.,16, 209–292 (1967).
V. G. Maz'ya and B. A. Plamenevskii, “On elliptic boundary-value problems in domains with a piecewise-smooth boundary,” in: Proc. Symp. on Continuum Mechanics and Related Problems of Analysis (Tbilisi 1971) [in Russian], Vol. 1, Metsniereba, Tbilisi (1973), pp. 171–181.
A. M. Il'in, “A boundary-value problem for a second-order elliptic equation in a domain with a narrow slit. I. The two-dimensional case,” Mat. Sb.,99 No. 4, 514–537 (1976).
V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, “Boundary-value problems in domains with thin crosspieces,” Funkts. Anal. Prilozhen.,17, No. 2, 20–29 (1982).
V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, Asymptotic Behavior of Solutions of Elliptic Boundary Value Problems Under Singular Perturbations of the Domain [in Russian], Tbilisi State Univ., Inst. Prikl. Mat., Tbilisi (1981).
I. A. Shishmarev, Introduction to the Theory of Elliptic Equations [in Russian], Moscow State Univ (1979).
Ya. S. Soibel'man, “A contribution to the Polya-Szegö problem of the computation of the asymptotics of the capacity of a circular condenser,” Manuscript deposited at VINITI, No. 2281-81 Dep.
R. Narasimhan, Analysis on Real and Complex Manifolds, Masson, Paris (1973).
Ya. S. Soibel'man, “The matching method in the condenser problem,” Manuscript deposited at VINITI, No. 4068-80 Dep.
A. E. H. Love, “Some electrostatic distributions in two dimensions,” Proc. London Math. Soc., Ser. 2,22, 337–369 (1924).
I. B. Simonenko and A. A. Chekulaeva, “On the capacity of a condensator consisting of infinite bands,” Izv. Vyssh. Uchebn. Zaved., Elektromekh., No. 4, 362–370 (1972).
S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Nauka, Moscow (1979).
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Rostov-on-the-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 6, pp. 167–181, November–December, 1984.
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Soibel'man, Y.S. Asymptotics of the capacity of a condenser with plates of an arbitrary shape. Sib Math J 25, 966–978 (1984). https://doi.org/10.1007/BF00968953
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DOI: https://doi.org/10.1007/BF00968953