Skip to main content
Log in

On capacity characteristics of condensers

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We introduce and study a one-parameter family of capacity characteristics of condensers in ℝp,p ≥ 3, that contains some known capacities as elements extremal with respect to the parameter. We establish new relations between the capacity characteristics of condensers and sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. F. W. Gehring, “Symmetrization of rings in space,”Trans. Am. Math. Soc.,101, No. 3, 499–519 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. M. Gol’dshtein and Yu. G. Reshetnyak,Introduction to the Theory of Functions with Generalized Derivatives and Quasiconfor-mal Mappings [in Russian], Nauka, Moscow 1983.

    Google Scholar 

  3. N. V. Zorii, “Functional characteristics of space condensers: their properties and relations,”Ukr. Mat. Zh.,39, No. 5, 565–573 (1987).

    MathSciNet  Google Scholar 

  4. N. V. Zorii, “On Newton capacities of condensers,” in:Problems of Analysis and Approximations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 67–75.

    Google Scholar 

  5. A. A. Grigor’yan, “On Liouville theorems for harmonic functions with finite Dirichlet integrals,”Mat. Sb.,132, No. 4, 496–516 (1987).

    MathSciNet  Google Scholar 

  6. W. P. Ziemer, “Extremal length andp-capacity,”Mich. Math. J.,16, No. 1, 43–51 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  7. Z. Hesse, “Ap-extremal length andp-capacity equality,”Ark. Mat.,13, No. 1, 131–144 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  8. N. S. Landkof,Foundations of Modern Potential Theory, Springer, Berlin 1972.

    MATH  Google Scholar 

  9. B. Fuglede, “On the theory of potentials in locally compact spaces,”Acta Math.,103, No. 3–4, 139–215 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  10. B. Fuglede, “Extremal length and functional completion,”Acta Math.,98, No. 3–4, 171–219 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  11. N. V. Zorii, “A noncompact variational problem in the theory of Riesz potentials. I,”Ukr. Mat. Zh.,47, No. 10, 1350–1360 (1995).

    Article  MathSciNet  Google Scholar 

  12. N. V. Zorii, “A noncompact variational problem in the theory of Riesz potentials. II,”Ukr. Mat. Zh.,48, No. 5, 603–613 (1996).

    Article  MathSciNet  Google Scholar 

  13. N. V. Zorii, “The problem of minimization of energy for space condensers and Riesz kernels,”Ukr. Mat. Zh.,41, No. 1, 34–41 (1989).

    Article  MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zorii, N.V. On capacity characteristics of condensers. Ukr Math J 48, 1889–1903 (1996). https://doi.org/10.1007/BF02375375

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02375375

Keywords

Navigation