In this paper, we establish a decomposition theorem for polyharmonicfunctions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichl...
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In this paper, we establish a decomposition theorem for polyharmonicfunctions 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 polyharmonicfunctions (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. (C) 2009 Elsevier Inc. All rights reserved.
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