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 APM  Vol.5 No.14 , December 2015
Lp Polyharmonic Dirichlet Problems in the Upper Half Plane
Kanda Pan*
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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.
Keywords: Dirichlet Problem, Polyharmonic Function, Higher Order Poisson Kernels, Higher Order Pompeiu Operators, Non-Tangential Maximal Function, Uniqueness
Cite this paper: Pan, K. (2015) Lp Polyharmonic Dirichlet Problems in the Upper Half Plane. Advances in Pure Mathematics, 5, 828-834. doi: 10.4236/apm.2015.514077.
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