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
Permanent link: http://hdl.handle.net/10197/5492
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
Copyright (published version): 2010 Springer
Keywords: Cauchy problem;Goursat problem;Dirichlet problem;Holomorphic PDE;Polyharmonic function;Fischer decomposition;Jacobi polynomial;Khavinson-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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