ON POINCARÉ’S VARIATIONAL PROBLEM IN POTENTIAL THEORY

@inproceedings{Khavinson2005ONPV,
  title={ON POINCARÉ’S VARIATIONAL PROBLEM IN POTENTIAL THEORY},
  author={Dmitry Khavinson and Mihai Putinar and Harold S. Shapiro},
  year={2005}
}
One of the earliest attempts to rigorously prove the solvability of Dirichlet’s boundary value problem was based on seeking the solution in the form of a ”potential of double layer”, and this leads to an integral equation whose kernel is (in general) both singular and nonsymmetric. C. Neumann succeeded with this approach for smoothly bounded convex domains, and H. Poincaré, by a tremendous tour de force, showed how to push through the analysis for domains with sufficiently smooth boundaries but… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 40 REFERENCES

Compact linear operators on functional spaces with two norms

  • M. G. Krein
  • (Ukrainian), Sbirnik Praz. Inst. Mat. Akad. Nauk…
  • 1998
Highly Influential
8 Excerpts

Potentialtheoretische Untersuchungen

  • J. Plemelj
  • Teubner, Leipzig
  • 1911
Highly Influential
5 Excerpts

Foundations of Modern Potential Theory

  • N. S. Landkof
  • Die Grundlehren der mathematischen Wissenschaften…
  • 1972
Highly Influential
4 Excerpts

The Kernel Function and Conformal Mapping

  • S. Bergman
  • 2nd ed. , Mathematical Surveys. 5, Providence, R…
  • 1970
Highly Influential
8 Excerpts

Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen

  • D. Hilbert
  • Leipzig, , reprint Chelsea, New York
  • 1953
Highly Influential
22 Excerpts

Über das Neumann-Poincarésche Problem für ein Gebiet mit Ecken

  • T. Carleman
  • Almquist and Wiksells, Uppsala
  • 1916
Highly Influential
6 Excerpts

Sur une classe d’équations fonctionnelles

  • I. Fredholm
  • Acta Math. 27
  • 1903
Highly Influential
22 Excerpts

La méthode de Neumann et le problème de Dirichlet

  • H. Poincaré
  • Acta Math. 20
  • 1897
Highly Influential
4 Excerpts

Fredholm eigenvalues and Grunsky matrices

  • M. Schiffer
  • Ann. Polonici Math. 39
  • 1981
Highly Influential
6 Excerpts

Foundations of Potential Theory

  • O. D. Kellogg
  • J. Springer, Berlin
  • 1929
Highly Influential
4 Excerpts

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