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A solution of the biharmonic dirichlet problem by means of hypercomplex analytic functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 561)

Keywords

  • Bijective Mapping
  • Zero Divisor
  • Projection Parallel
  • Cauchy Integral Formula
  • Riemann Equation

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References

  1. J. Horvath, A Generalization of the Cauchy-Riemann Equations, Contributions to Differential Equations, Volume I, Interscience Publishers, 1963, 39–58.

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  2. J. Edenhofer, Analytische Funktionen auf Algebren, TU München, 1973, Dissertation.

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  3. W. Eichhorn, Funktionentheorie in Algebren über dem reellen Zahlenkörper und ihre Anwendung auf partielle Differentialgleichungen, Würzburg, 1961, Dissertation.

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  4. R. Fueter, Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen, Comment. Math. Helvet., 8,1935, 371.

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  5. O.D. Kellogg, Harmonic functions and Greens integral, Transactions of the Americ. Math. Society 13, 1912, 109–132.

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  6. E. Lammel, Über eine zur Differentialgleichung \((a_O \tfrac{{\partial ^n }}{{\partial x^n }} + a_1 \tfrac{{\partial ^n }}{{\partial x^{n - 1} \partial y}} + ... + \tfrac{{\partial ^n }}{{\partial x^n }})\) U(x,y)=O gehörige Funktionentheorie I, Math. Ann. 122, 1950/51, 109–126.

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© 1976 Springer-Verlag

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Edenhofer, J. (1976). A solution of the biharmonic dirichlet problem by means of hypercomplex analytic functions. In: Meister, V.E., Wendland, W.L., Weck, N. (eds) Function Theoretic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087636

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  • DOI: https://doi.org/10.1007/BFb0087636

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08054-1

  • Online ISBN: 978-3-540-37536-4

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