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

2015/07/30 by Kanda Pan, Pan, Kanda, Guoan Guo +3
Mathematics · #31B10 #31B30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:31B10 #msc:31B30

paper · pdf · doi:10.48550/arxiv.1507.08668

20 papges

arxiv created 2015/07/30 · arxiv updated 2015/08/03

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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