In the paper, the existence and uniqueness of the extremal functions for the condenser capacity and the module of a family of curves in Finsler spaces are proved, and a relation between the condenser capacity and the module of the family of separating surfaces in Finsler spaces is established.
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References
H. Gaeskii et al., Nonlinear Operator Equations and Operator Differential Equations [in Russian], Moscow (1978).
V. M. Goldshtein and Yu. G. Reshetnyak, Introduction to the Theory of Functions With Generalized Derivatives and Quasiconformal Mappings [in Russian], Moscow (1983).
Yu. V. Dymchenko, “Equality of the capacity and module of a condenser in Finsler spaces,” Matem. Zametki, 85, No. 4, 594–602 (2009).
H. Rund, The Differential Geometry of Finsler Spaces [Russian translation], Moscow (1981).
V. A. Shlyk, “The condenser capacity and the module of the separating surfaces,” Zap. Nauchn. Semin. POMI, 185, 168–182 (1990).
B. Fuglede, “Extremal length and functional completion,” Acta Math., 126, No. 3, 171–219 (1957).
M. Ohtsuka, Extremal Length and Precise Functions (GAKUTO Int. Ser. Math. Sci. Appl., 19), Gakkōtosho, Tokyo (2003).
Z. Shen, Lectures on Finsler Geometry (Multivariate Analysis Ser.), World Scientific Publishing Company (2001).
W. P. Ziemer, “Extremal length and conformal capacity,” Trans. Amer. Math. Soc., 126, No. 3, 460–473 (1967).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 418, 2013, pp. 74–89.
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Dymchenko, Y.V. A Relation Between the Condenser Capacity and the Module of Separating Surfaces in Finsler Spaces. J Math Sci 200, 559–567 (2014). https://doi.org/10.1007/s10958-014-1944-6
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DOI: https://doi.org/10.1007/s10958-014-1944-6