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Dirichlet Problems for Inhomogeneous Complex Mixed-Partial Differential Equations of Higher order in the Unit Disc: New View

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Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 205))

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Abstract

In this paper, we discuss some Dirichlet problems for inhomogeneous complex mixed-partial differential equations of higher order in the unit disc. Using higher-order Pompeiu operators T m,n, we give some special solutions for the inhomogeneous equations. The solutions of homogeneous equations are given on the basis of decompositions of polyanalytic and polyharmonic functions. Combining the solutions of the homogeneous equations and special solutions, we obtain all solutions of the inhomogeneous equations.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    H. Begehr

  2. Department of Mathematics, Jinan University, Guangzhou, 510632, China

    Zhihua Du

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Ning Wang

Authors
  1. H. Begehr
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  2. Zhihua Du
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  3. Ning Wang
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Bert-Wolfgang Schulze

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Begehr, H., Du, Z., Wang, N. (2009). Dirichlet Problems for Inhomogeneous Complex Mixed-Partial Differential Equations of Higher order in the Unit Disc: New View. In: Schulze, BW., Wong, M.W. (eds) Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations. Operator Theory: Advances and Applications, vol 205. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0198-6_6

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