On the condensers with variable plates, potential levels and domain of definition |
Dubinin V., Kim V. Yu. |
2022, issue 1, P. 55-60 DOI: https://doi.org/10.47910/FEMJ202205 |
Abstract |
The asymptotic formula is obtained for the capacity of a generalized condenser when parts of its plates contract to prescribed points. We consider condenser with variable potential levels and a set of definition that tends to a predetermined domain. |
Keywords: asymptotic formula, conformal capacity, condenser, Green’s function |
Download the article (PDF-file) |
References |
[1] G. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, Fiz-matlit, M., 1962. [2] L. V. Ahlfors, A. Beurling, “Conformal invariants and function-theoretic null-sets”, Acta math., 83:1/2 (1950), 101–129. [3] V. K. Kheiman, Mnogolistnye funktsii, Izd-vo inostr. lit., M., 1960. [4] Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniia, Izd-vo inostr. lit., M., 1962. [5] V. G. Kuz'mina, “Metody geometricheskoi teorii funktsii. II”, Algebra i analiz, 9:5 (1997), 1–50. [6] A. Iu. Solynin, “Moduli i ekstremal'no-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86. [7] V. N. Dubinin, “Asimptotika modulia vyrozhdaiushchegosia kondensatora i nekotorye ee primeneniia”, Zap. nauchn. sem. POMI, 237 (1997), 56–73. [8] V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Birkhauser/Springer, Basel, 2014. [9] V. N. Dubinin, M. Vuorinen, “Robin functions and distortion theorems for regular map-pings”, Math. Nachr., 283:11 (2010), 1589–1602. [10] V. N. Dubinin, “Asimptotika emkosti kondensatora s peremennymi urovniami potentsiala”, Sib. matem. zhurn., 61:4 (2020), 796–802. [11] M. Schi?er, “Some recent developments in the theory of conformal mapping”, Appendix to: R. Courant, Dirichlet’s principle, conformal mapping, and minimal surfaces, Interscience Publishers, Inc., New York, 1950, 249–323. |