Iterated Dirichlet problem for the higher order Poisson equation

  • H. Begehr
  • T. Vaitekhovich Belarusian State University,
Keywords: Polyharmonic equation, Iterated Dirichlet problem, Polyharmonic Green functions


Convoluting the harmonic Green function with itself consecutively leads to a polyharmonic Green function suitable to solve an iterated Dirichlet problem for the higher order Poisson equation. The procedure works in any regular domain and is not restricted to two dimensions. In order to get explicit expressions however the situation is studied in the complex plane and sometimes in particular the unit disk is considered.

Author Biographies

H. Begehr

Math. Institut,

FU Berlin, Arnimallee 3,

D-14195 Berlin, Germany

T. Vaitekhovich, Belarusian State University,
Mech.-Math. Department,
220050, Nezavisimosty av., 4, Minsk, Belarus