Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
|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||Journal:||Computational Methods and Function Theory||Volume:||10||Issue:||2||Start page:||519||End page:||554||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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