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<i>L<sup>p</sup></i> Polyharmonic Dirichlet Problems in the Upper Half Plane
Department of Mathematics, Jinan University, Guangzhou, China
- 1 Department of Mathematics, Jinan University, Guangzhou, China
Advances in Pure Mathematics·Volume 05 (2015)·Pages 828–834·Published 7 December 2015·DOI10.4236/apm.2015.514077
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Abstract
In this article, a class of Dirichlet problem with L p 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.
KeywordsDirichlet ProblemPolyharmonic FunctionHigher Order Poisson KernelsHigher Order Pompeiu OperatorsNon-Tangential Maximal FunctionUniqueness
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