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Lp Polyharmonic Dirichlet Problems in the Upper Half Plane

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DOI: 10.4236/apm.2015.514077    4,521 Downloads   4,849 Views  
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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.

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The authors declare no conflicts of interest.

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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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