An inhomogeneous polyharmonic Dirichlet problem with boundary data in the upper half-plane

Abstract

In this paper, an inhomogeneous Dirichlet problem with data for the polyharmonic equation is investigated in the upper half-plane. By using higher order Poisson kernels and Pompeiu operators, which are respectively due to Du et al. [Du Z, Qian T, Wang J. polyharmonic Dirichlet problems in regular domains II: the upper half plane. J Differ Equ. 2012;252:1789–1812] as well as Begehr and Hile [Begehr H, Hile G. A hierarchy of integral operators. Rocky Mountain J Math. 1997;27:669–706], an integral representation for the unique solution is given under certain assumptions.