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arXiv · 1507.08668

An inhomogeneous polyharmonic Dirichlet problem with $L^p$ boundary data in the upper half-plane

Kanda Pan·Guoan Guo·Zhihua Du
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Abstract

In this paper, it is investigated for an inhomogeneous Dirichlet problem with $L^p$ boundary data for polyharmonic equation in the upper half-plane. By using higher order Poisson kernels and Pompeiu operators, which are respectively due to Du, Qian and Wang [Z. Du, T. Qian and J. Wang, {\it $L^{p}$ polyharmonic Dirichlet problems in regular domains II: The upper half plane}, J. Differential Equations 252(2012), 1789-1812] as well as Begehr and Hile [H. Begehr and G. Hile, {\it A hierarchy of integral operators}, Rocky Mountain J. Math. 27(1997), 669-706], it is given that the unique integral representation solution under some certain estimates.

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Kanda Pan, Guoan Guo, Zhihua Du. 2015-07-30. An inhomogeneous polyharmonic Dirichlet problem with $L^p$ boundary data in the upper half-plane. https://arxiv.org/abs/1507.08668

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