The Dirichlet problem when the boundary function is entire

DOI10.1016/j.jmaa.2003.11.016zbMath1087.32002OpenAlexW2076339897MaRDI QIDQ1433362

David H. Armitage

Publication date: 15 June 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.11.016

zbMATH Keywords

Dirichlet problementire functiongrowth rateharmonic extension

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Entire functions of several complex variables (32A15)

Related Items (8)

A characterization of the Khavinson-Shapiro conjecture via Fischer operators ⋮ Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations ⋮ The Khavinson-Shapiro conjecture and polynomial decompositions ⋮ A Fischer type decomposition theorem from the apolar inner product ⋮ Dirichlet's problem with entire data posed on an ellipsoidal cylinder ⋮ The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces ⋮ On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Cites Work

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• Growth of entire harmonic functions in \(R^n,\;n\geq 2\)
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• Dirichlet's Problem When the Data is an Entire Function
• On Brelot-Choquet Axial Polynomials

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