Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations

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Title: Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
Authors: Render, Hermann
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Date: Jan-2011
Abstract: n this paper we survey recent results about Fischer decomposi- tions of polynomials or entire functions and their applications to holomorphic partial di erential equations. We discuss Cauchy and Goursat problems for the polyharmonic operator. Special emphasis is given to the Khavinson-Shapiro conjecture concerning polynomial solvability of the Dirichlet problem.
Type of material: Journal Article
Publisher: Springer
Journal: Computational Methods and Function Theory
Volume: 10
Issue: 2
Start page: 519
End page: 554
Copyright (published version): 2010 Springer
Keywords: Cauchy problemGoursat problemDirichlet problemHolomorphic PDEPolyharmonic functionFischer decompositionJacobi polynomialKhavinson-Shapiro conjecture
DOI: 10.1007/BF03321779
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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