An inhomogeneous polyharmonic Dirichlet problem with $L^p$ boundary data in the upper half-plane
Analysis of PDEs
2015-08-03 v1
Abstract
In this paper, it is investigated for an inhomogeneous Dirichlet problem with 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 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.
Cite
@article{arxiv.1507.08668,
title = {An inhomogeneous polyharmonic Dirichlet problem with $L^p$ boundary data in the upper half-plane},
author = {Kanda Pan and Guoan Guo and Zhihua Du},
journal= {arXiv preprint arXiv:1507.08668},
year = {2015}
}
Comments
20 papges