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Polyharmonic dirichlet problems

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Abstract

A certain Dirichlet problem for the inhomogeneous polyharmonic equation is explicitly solved in the unit disc of the complex plane. The solution is obtained by modifying the related Cauchy-Pompeiu representation with the help of a polyharmonic Green function.

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Authors and Affiliations

  1. I. Math. Inst., FU Berlin, Arnimallee 3, D-14195, Germany

    H. Begehr

  2. Department of Applied Mathematics, Hanoi University of Technology, Khoa Toan Ung Dung, Hanoi, Vietnam

    T. N. H. Vu

  3. Department of Mathematics, Wuhan University, Wuhan, 430072, P.R. China

    Z. -X. Zhang

Authors
  1. H. Begehr
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  2. T. N. H. Vu
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  3. Z. -X. Zhang
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Dedicated to Prof. S.M. Nikol’skii on the occasion of his 100th birthday and to the memory of P.G.L. Dirichlet on the occasion of his 200th birthday

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Begehr, H., Vu, T.N.H. & Zhang, Z.X. Polyharmonic dirichlet problems. Proc. Steklov Inst. Math. 255, 13–34 (2006). https://doi.org/10.1134/S0081543806040031

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  • DOI: https://doi.org/10.1134/S0081543806040031

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