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

  • H. Begehr
  • Zhihua Du
  • Ning Wang
Part of the Operator Theory: Advances and Applications book series (OT, volume 205)

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.

Keywords

Dirichlet problems higher order Pompeiu operators higher-order Poisson kernels decomposition polyanalytic functions polyharmonic functions inhomogeneous equations unit disc 

Mathematics Subject Classification (2000)

Primary 30G30 Secondary 45E05 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • H. Begehr
    • 1
  • Zhihua Du
    • 2
  • Ning Wang
    • 3
  1. 1.Institute of MathematicsFreie Universität BerlinBerlinGermany
  2. 2.Department of MathematicsJinan UniversityGuangzhouChina
  3. 3.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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