Geodesic
Generalized capacities and polyhedral surfaces
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 148-178
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In the paper, we apply the theory of extremal length of vector measures to establish that the generalized condenser capacity in the sense of Aikawa and Ohtsuka is related to the module of a family of surfaces separating the condenser's plates and no intersecting prescribed set. We prove that the system of the polyhedral surfaces from the above family is sufficient to approximate the module of this family. Bibl. 17 titles. 
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P. A. Pugach; V. A. Shlyk. Generalized capacities and polyhedral surfaces. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 148-178. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a10/

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

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

[3] B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal functions”, Trans. Amer. Math. Soc., 192 (1972), 207–226 | DOI | MR

[4] I. N. Dëmshin, V. A. Shlyk, “Kriterii ustranimykh mnozhestv dlya prostranstv $L^1_{p,w}$, $FD^{p,w}$”, Dokl. RAN, 343:5 (1995), 550–552 | MR

[5] M. Ohtsuka, “Extremal length and precise functions”, GAKUTO International Journal, Advances in Math. Sciences and Appl., 19 (2003), 1–343 | MR

[6] E. Dzhusti, Minimalnye poverkhnosti i funktsii ogranichennoi variatsii, M., 1989 | MR

[7] V. G. Mazya, Prostranstva S. L. Soboleva, L., 1985 | MR | Zbl

[8] L. K. Evans, R. F. Gariepi, Teoriya mery i tonkie svoistva funktsii, Novosibirsk, 2002

[9] W. P. Ziemer, “Extremal length and conformal capacity”, Trans. Amer. Math. Soc., 126:3 (1967), 460–473 | DOI | MR | Zbl

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

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

[12] V. M. Goldshtein, Yu. G. Reshetnyak, Vvedenie v teoriyu funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, M., 1983 | MR

[13] N. Burbaki, Integrirovanie. Vektornoe integrirovanie. Mera Khaara, Nauka, M., 1970 | MR

[14] E. Lib, M. Loss, Analiz, Novosibirsk, 1998

[15] V. M. Miklyukov, Vvedenie v negladkii analiz, Izd-vo VolGU, Volgograd, 2008

[16] V. V. Aseev, “$NED$-mnozhestva, lezhaschie v giperploskosti”, Sib. mat. zh., 50:5 (2009), 967–986 | MR | Zbl

[17] H. Federer, W. H. Fleming, “Normal and integral currents”, Ann. Math., 72 (1960), 458–520 | DOI | MR | Zbl