Precise estimate of the 2-capacity of a condenser
Received: 26 January 1988 DOI:
Cite this article as: Zorii, N.V. Ukr Math J (1990) 42: 224. doi:10.1007/BF01071019 Abstract
For quite a large class of condensers E (including, in particular, all space annuli) greatest lower bounds for their 2-capacity are obtained in terms of the Newtonian capacity of certain sets associated with E. A class of condensers for which equality is achieved in the bound is described completely.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 253–257, February, 1990.
F. W. Gehring, “Inequalities for condensers, hyperbolic capacity, and extremal lengths,” Mich. Math. J.,
18, No. 1, 1–20 (1971).
N. S. Landkof, Foundations of Modern Potential Theory [in Russian], Nauka, Moscow (1966).
N. V. Zorii, “Some functional characteristics of space condensers and relations among them,” Preprint, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1985).
G. D. Anderson and M. K. Vamanamurthy, “The Newtonian capacity of a space condenser,” Indiana Univ. Math. J.,
34, No. 4, 753–776 (1985).
N. V. Zorii, Condensers, Charges on Them: Estimates of Energy and Capacity under Re-arrangements of Condensers [in Russian], Candidate's Dissertation, Fiz.-Mat. Nauk, Kiev (1980).
N. V. Zorii, “The minimum energy problem for space condensers,” Preprint, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1985).
H. Kloke, “Some inequalities for the capacity of plane condensers,” Resultate Math.,
9, Nos. 1–2, 82–94 (1986).
N. V. Zorii, “The minimum Green's energy problem for space condensers,” in: Problems in Analysis and Differential Topology [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1988), pp. 39–47.
© Plenum Publishing Corporation 1990