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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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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

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