Decompositions of functions and Dirichlet problems in the unit disc |
| |
Authors: | Zhihua Du Guoan Guo |
| |
Institution: | a Department of Mathematics, Jinan University, Guangzhou 510632, China b School of Natural Sciences, Nanjing University of Posts and Telecommunications, Nanjing 210046, China c School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
| |
Abstract: | In this paper, we establish a decomposition theorem for polyharmonic functions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichlet problem for polyharmonic functions (PHD problem) and give a unified expression for a class of kernel functions associated with the solution in the case of the unit disc introduced by Begehr, Du and Wang. In addition, we also discuss some quasi-Dirichlet problems for homogeneous mixed-partial differential equations of higher order. It is worthy to note that the decomposition theorem in the present paper is a natural extension of the Goursat decomposition theorem for biharmonic functions. |
| |
Keywords: | Decomposition of polyharmonic functions Polyharmonic functions Polyanalytic functions Dirichlet problem |
本文献已被 ScienceDirect 等数据库收录! |
|