Lp Polyharmonic Dirichlet Problems in the Upper Half Plane

DOI: 10.4236/apm.2015.514077   PDF   HTML   XML   4,631 Downloads   5,001 Views  

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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