Skip to main content
SpringerLink
Log in

Planar dielectric potential functions

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. M. Schiffer, The Fredholm Eigenvalues of Plane Domains,Pacific J. Math.,7 (1957), 1187–1225.

    MATH  MathSciNet  Google Scholar 

  2. M. Schiffer. The Fredholm Eigenvalues of Multiply Connected Domains,Pacific J. Math.,9 (1959), 211–269.

    MATH  MathSciNet  Google Scholar 

  3. J. L. Troutman, Eigenvalues and Eigenfunctions of a Class of Potential Operators in the Plane, Doctoral Thesis, Stanford University, 1964.

  4. J. L. Troutman. The Logarithmic Potential Operator,Illinois J. Math.,11 (1967), 365–374.

    MATH  MathSciNet  Google Scholar 

  5. J. L. Troutman. The Logarithmic Eigenvalues of Plane Sets,Illinois J. Math.,13 (1969), 95–107.

    MATH  MathSciNet  Google Scholar 

  6. F. Y. Maeda, Normal Derivatives on an Ideal Boundary,J. Sci. Hiroshima Univ. Ser. A—I,28 (1964), 113–131.

    MATH  Google Scholar 

  7. F. Y. Maeda. Boundary Value Problems for the EquationΔu−qu=0 with respect to an Ideal Boundary,J. Sci. Hiroshima Univ. Ser. A—I,32 (1960), 85–146.

    Google Scholar 

  8. I. N. Vekua, Generalized Analytic Functions. Reading, Massachusetts: Addison Wesley (1962), 4–75.

    MATH  Google Scholar 

  9. A. P. Calderón and A. Zygmund, On the Existence of certain Singular Integrals,Acta. Math.,88 (1952), 85–139.

    Article  MATH  MathSciNet  Google Scholar 

  10. O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen. Berlin: Springer (1965), 222–225.

    MATH  Google Scholar 

  11. H. Royden, Real Analysis. New York: Macmillan (1963), 52.

    MATH  Google Scholar 

  12. L. Lichtenstein, Neuere Entwicklung der Potentialtheorie,Encyk. d. Math. Wiss. II, C. 3 (1918), 197–214.

    Google Scholar 

  13. J. Kral, On the Logarithmic Potential of the Double Distribution,Czech. Math. J.,14 (89) (1964), 306–321.

    MathSciNet  Google Scholar 

  14. J. Kral, Non-tangential limits of the Logarithmic Potential,Czech. Math. J.,14 (89) (1964), 455–482.

    MathSciNet  Google Scholar 

  15. F. Riesz and B. Sz. Nagy, Functional Analysis. New York: Ungar (1955), 227–246.

    Google Scholar 

  16. H. Weyl, The Method of orthogonal projection in potential theory,Duke Math. J.,7, (1940), 411–444.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. L. Troutman, The Dielectric Potential Operator (to appear).Arch. for Rat'l. Mech. and Analysis.

  18. L. I. Hedberg, Approximation in the mean by analytic functions. (To appear)

  19. S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics (Translations of Math. Monographs, 7). Am. Math. Soc., Providence, R. I. (1963), 33–42.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, Syracuse, N. Y., U.S.A.

    John L. Troutman

Authors
  1. John L. Troutman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Troutman, J.L. Planar dielectric potential functions. J. Anal. Math. 25, 1–48 (1972). https://doi.org/10.1007/BF02790030

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790030

Keywords

Search

Navigation