Abstract
The uniqueness of the extremal function for the p-capacity of a condenser is established. Bibliography: 7 titles.
Similar content being viewed by others
References
V. A. Shlyk, “The capacity of a condenser and the module of a family of separating surfaces,”Zap. Nauchn. Semin. LOMI,185, 168–182 (1990).
F. W. Gehring, “Rings and quasiconformal mappings in space,”Trans. Am. Math. Soc.,103, 353–393 (1962).
V. M. Gol'dshtein and Yu. G. Reshetnyak,Introduction to the Theory of Functions with Generalized Derivatives and Quasiconformal Mappings [in Russian], Moscow (1983).
B. Fuglede, “Extremal length and functional completion,”Acta Math.,98, 171–219 (1957).
V. V. Aseev, “An example of an NED-set in Euclideann-space with positive (n-1)-dimensional Hausdorff measure,”Dokl. Akad. Nauk SSSR,216, 717–720 (1974).
V. A. Shlyk, “Normal domains and removable singularities,”Izv. Ross. Akad. Nauk, Ser. Mat.,57, No. 4, 93–117 (1993).
V. A. Shlyk, “On the equality of thep-capacity and thep-module,”Sib. Mat. Zh.,34, No. 6, 216–221 (1993).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 228–234.
Rights and permissions
About this article
Cite this article
Shlyk, V.A. Uniqueness of the extremal function for thep-capacity of a condenser. J Math Sci 89, 1072–1077 (1998). https://doi.org/10.1007/BF02358542
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02358542