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Cauchy, Goursat and Dirichlet Problems for Holomorphic Partial Differential Equations

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Abstract

In this paper we survey recent results about Fischer decompositions of polynomials or entire functions and their applications to holomorphic partial differential 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.

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    Hermann Render

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Render, H. Cauchy, Goursat and Dirichlet Problems for Holomorphic Partial Differential Equations. Comput. Methods Funct. Theory 10, 519–554 (2011). https://doi.org/10.1007/BF03321779

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