Skip to main content
SpringerLink
Log in

Elliptic operators and Choquet capacities

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Choquet capacities generated by solutions of certain elliptic partial differential equations are discussed. Bibliography: 11 titles.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. K. Hayman and P. B. Kennedy, Subharmonic Functions. Vol. I (London Mathematical Society Monographs, No. 9), Academic Press [Harcourt Brace Jovanovich, Publishers], London–New York (1976).

    MATH  Google Scholar 

  2. G. Choquet, “Theory of capacities,” Ann. Inst. Fourier, Grenoble, 5, 131–295 (1953–1954), (1955).

    MathSciNet  Google Scholar 

  3. V. G. Maz’ja, Sobolev Spaces, Springer-Verlag, Berlin (1985).

    MATH  Google Scholar 

  4. I. P. Mityuk, “An upper bound for the product of interior radii of domains, and covering theorems,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 39–47 (1987).

  5. I. P. Mityuk, “A lower bound on the sum of condenser capacities,” Ukr. Mat. Zh., 42, No. 3, 390–393 (1990).

    Article  MathSciNet  Google Scholar 

  6. I. P. Mityuk and A. Yu. Solynin, “Ordering of systems of domains and condensers in n-dimensional space,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 54–59 (1991).

  7. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin (2001).

    MATH  Google Scholar 

  8. A. Henrot, “Continuity with respect to the domain for the Laplacian: a survey. Shape design and optimization,” Control Cybernet., 23, No. 3, 427–443 (1994).

    MATH  MathSciNet  Google Scholar 

  9. A. Yu. Solynin, “Ordering of sets, the hyperbolimetric, and harmonic measure,” Zap. Nauchn. Semin. POMI, 237, 129–147 (1997).

    Google Scholar 

  10. A. F. Beardon and D. Minda, “The hyperbolimetric and geometric function theory,” in: Quasiconformal Mappings and their Applications, Narosa Publishing House, New Dehi, India (2007), pp. 10–56.

    Google Scholar 

  11. S. Agard, “Distortion theorems for quasiconformal mappings,” Ann. Acad. Sci. Fenn. Ser. AI Math., 413, 1–12(1968).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, U.S.A.

    A. Yu. Solynin

Authors
  1. A. Yu. Solynin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Solynin.

Additional information

Dedicated to the 80th anniversary of I. P. Mityuk’s birthday

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 149–156.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solynin, A.Y. Elliptic operators and Choquet capacities. J Math Sci 166, 210–213 (2010). https://doi.org/10.1007/s10958-010-9861-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-010-9861-9

Keywords

Search

Navigation