Pacific Journal of Mathematics

A partial differential equation arising in conformal mapping.

P. R. Garabedian

Article information

Source
Pacific J. Math., Volume 1, Number 4 (1951), 485-524.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103052020

Mathematical Reviews number (MathSciNet)
MR0046440

Zentralblatt MATH identifier
0045.05102

Subjects
Primary: 30.0X

Citation

Garabedian, P. R. A partial differential equation arising in conformal mapping. Pacific J. Math. 1 (1951), no. 4, 485--524. https://projecteuclid.org/euclid.pjm/1103052020


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References

  • [1] S. Bergman, Sur es functions orthogonales de plusieurs variables complexes, avec les applicationsa la theorie des junctionsanaltiques,Gauthier-Villars, Paris, 1947.
  • [2] S. Bergman, Zwei Satze uber Funktionen von zwei komplexen Veranderlichen, Math. Ann. 100 (1928),399-410.
  • [3] S. Bergman and M. Schiffer, A representation of Green*s and Neumann*s functions in the theory of partial differentialequations of second order^ Duke Math, J. 14 (1947), 609-638.
  • [4] S. Bergman and M. Schiffer, On Green's and Neumann's functions in the theory of partial differential equations, Bull. Amer. Math. Soc. 53 (1947),1141-1151.
  • [5] S. Bergman and M. Schiffer, Kernel functions in the theory of partial differential equations of elliptic type, Duke Math. J. 15 (1948),535-566.
  • [6] S. Bergman and M. Schiffer, Kernel functions and conformal mapping, to appear in the Duke Math. J.
  • [7] K. 0. Friedrichs, On certain inequalities and characteristicvalue problems for ana- lytic functions and for functionsof two variables, Trans. Amer. Math. Soc. 41 (1937), 321-364.
  • [8] P. R. Garabedian, Schwarz'slemma and the Szego kernel function, Trans. Amer. Math. Soc. 67 (1949), 1-35.
  • [9] P. R. Garabedian, A new proof of the Riemann mapping theorem, to appear shortly.
  • [10] P. R. Garabedian and M. Schiffer, On existencetheorems of potential theory and conformal mapping, Ann. of Math. 52 (1950), 164-187.
  • [11] J. Hadamard, Memoire sur le probleme d'analyserelatif a I* equilibre des plaques elastiques encastrees, Memoires presentes par divers savants a l'Academie des Sciences, (2) 33 (1908).
  • [12] O. Lehto, Anwendung orthogonaler Systemeauf gewissefunktionentheoretische Extremal-und Abbildungsprobleme, Ann. Acad. Sci. Fennicae, Ser. A. I. Math.-Phys. no. 59 (1949).
  • [13] M. Schiffer, The kernel function of an orthonormal system, Duke Math. J. 13 (1946), 529-540.
  • [14] M. Schiffer and G. Ssego, Virtual mass and polarization, Trans. Amer. Math. Soc. 67 (1949), 130-205.
  • [15] G. Szego, Orthogonal polynomials, Amer. Math. Soc. Coll. Pub., vol. 23, New York, 1939.
  • [16] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Coll. Pub., vol. 20, New York, 1935.
  • [17] S. Zaremba, L'equation biharmonique et une class remarquable de fonctions fonda- mentales harmoniques, Bull. International de l'Academie des Sciences de Cracovie (1907), 147-196.
  • [18] S. Zaremba, Sur le calcul numerique des fonctions demandees dans le probleme de Dirichlet et le probleme hydrodynamique, Bull. International de l'Academie des Sciences de Cracovie (1908), 125-195.
  • [19] G. Fichera,Sull'esistenzadelle funzioni potenziali nei problemi dellafisica matematica, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat, Nat. (8) 2, (1947), 527-532.
  • [20] G. Fichera, Teorema d'esistenzaper il problema bi-iperarmonico, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 5 (1948), 319-324.
  • [21] G. Fichera, On some general integration methods employed in connection with linear differential equations, J. of Math, and Phys., vol. 31 (1950), 59-68.