Begehr, H. and Gaertner, E. (2007) A Dirichlet Problem for the Inhomogeneous Polyharmonic Equations in the Upper Half Plane. Georgian Mathematical Journal, 14, 33-52.

has been cited by the following article:

• TITLE: Lp Polyharmonic Dirichlet Problems in the Upper Half Plane

  AUTHORS: Kanda Pan

  KEYWORDS: Dirichlet Problem, Polyharmonic Function, Higher Order Poisson Kernels, Higher Order Pompeiu Operators, Non-Tangential Maximal Function, Uniqueness

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.14, December 11, 2015

  ABSTRACT: In this article, a class of Dirichlet problem with Lp boundary data for poly-harmonic function in the upper half plane is mainly investigated. By introducing a sequence of kernel functions called higher order Poisson kernels and a hierarchy of integral operators called higher order Pompeiu operators, we obtain a main result on integral representation solution as well as the uniqueness of the polyharmonic Dirichlet problem under a certain estimate.