Skip to main content
Log in

Representation and Uniqueness Theorems for Polyharmonic Functions

  • Published:
Journal d Analyse Mathematique Aims and scope

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.

References

  1. E. Almansi, Sulle integrazione dell’ equazione differenciale Δ2n = 0, Annali di Matematica, s.3, 2 (1899), 1–59.

    Article  MATH  Google Scholar 

  2. N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1983.

    MATH  Google Scholar 

  3. M. A. Atahodzhaev and Z.A. Ahmedov, A problem for the biharmonic equation, Izv. Akad. Nauk Uz. SSR, ser. Fiz.-Mat. Nauk, no.1 (1980), 3–9 (Russian).

  4. A.V. Bitsadze, On polyharmonic functions, Dokl. Akad. Nauk SSSR 294 (1987), 521–525.

    MathSciNet  Google Scholar 

  5. J. Edenhoffer, Integraldarstellungen einer m-polyharmonischen Funktion, deren Funktionswerte und erste m − 1 Normalableitungen auf einer Hypersphäre gegeben sind, Math. Nachr. 68 (1975), 105–113.

    Article  MathSciNet  Google Scholar 

  6. P.R. Garabedian, A partial differential equation arising in conformal mapping, Pacific J. Math. 1 (1951), 485–524.

    Article  MATH  MathSciNet  Google Scholar 

  7. W.K. Hayman and P.B. Kennedy, Subharmonic Functions, Vol. 1, Academic Press, New York, 1976.

    MATH  Google Scholar 

  8. D.I. Kunchev, A harmonic function that deviates least from a given function that is continuous in the disk, Dokl. Akad. Nauk BSSR 29 (1985), 293–295 (Russian).

    MATH  MathSciNet  Google Scholar 

  9. J.W. Milnor, Topology from the Differentiable Viewpoint, The University Press of Virginia, Charlottesville, 1965.

    MATH  Google Scholar 

  10. M. Ortel, An access theorem for analytic functions, preprint.

  11. A. Sard, The measure of the critical points of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883–890.

    Article  MATH  MathSciNet  Google Scholar 

  12. E.P. Smyrnelis, Une propriété de moyenne des fonctions biharmoniques, Bull. Soc. Math. France (2) 109 (1985), 103–111.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hayman, W.K., Korenblum, B. Representation and Uniqueness Theorems for Polyharmonic Functions. J. Anal. Math. 60, 113–133 (1993). https://doi.org/10.1007/BF03341969

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03341969

Keywords

Navigation