Geodesic
Capacity of polycondensor and the module of the family of vector measure
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 56-68 
Yu. V. Dymchenko; V. A. Shlyk. Capacity of polycondensor and the module of the family of vector measure. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 56-68. http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a4/
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     title = {Capacity of polycondensor and the module of the family of vector measure},
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     year = {2009},
     volume = {371},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper considers the capacity of a polycondenser and the modules of families of measures related to curves connecting the polycondenser's plates. It is proved that these quantities are equal. Also a relation between the polycondenser's capacity and the module of a family of vector measures connected with a class of functions admissible for the polycondinser's capacity is established. The results obtained generalize the corresponding results by M. Ohtzuka and H. Aikava. Bibl. – 7 titles.

[1] V. V. Aseev, B. Yu. Sultanov, Moduli polikondensatorov i izomorfizmy prostranstv sledov nepreryvnykh funtsii klassa $W^1_n$, Preprint, AN SSSR, Sib. otd., In-t mat., Novosibirsk, 1989

[2] U. Rudin, Funktsionalnyi analiz, M., 1975 | MR

[3] V. A. Shlyk, “Emkost kondensatora i modul semeistva razdelyayuschikh poverkhnostei”, Zap. nauchn. semin. LOMI, 185, 1990, 168–182 | MR | Zbl

[4] I. Ekland, R. Temam, Vypuklyi analiz i variatsionnye problemy, M., 1979 | MR

[5] H. Aikawa, M. Ohtsuka, “Extremal length of vector measures”, Ann. Acad. Sci. Fenn. Math., 24 (1999), 61–88 | MR | Zbl

[6] B. Fuglede, “Extremal length and functional completion”, Acta Math., 126:3 (1957), 171–219 | DOI | MR

[7] M. Ohtsuka, Extremal length and precise functions, GAKUTO Intern. Series. Math. Sci. and Appl., 19, 2003, 343 pp. | MR | Zbl