Polynomial solutions to Dirichlet problems

DOI10.1090/S0002-9939-00-05512-XzbMath0954.31002OpenAlexW1556636758MaRDI QIDQ4510066

David Siegel, Marc Chamberland

Publication date: 19 October 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05512-x

zbMATH Keywords

Dirichlet problemLaplacian operatorpolynomial solution

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items (14)

The Khavinson-Shapiro conjecture and the Bergman projection in one and several complex variables ⋮ Range descriptions for the spherical mean Radon transform ⋮ Dirichlet's problem and complex lightning bolts ⋮ A characterization of the Khavinson-Shapiro conjecture via Fischer operators ⋮ Harmonic divisors and rationality of zeros of Jacobi polynomials ⋮ Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations ⋮ The Khavinson-Shapiro conjecture and polynomial decompositions ⋮ Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions ⋮ On the solution of the Dirichlet problem with rational holomorphic boundary data ⋮ The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces ⋮ Harmonic Functions in Slabs and Half-Spaces ⋮ On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc ⋮ On the classical Dirichlet problem in the plane with rational data ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Cites Work

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• The mixed Cauchy problem for holomorphic partial differential operators
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• Dirichlet's Problem When the Data is an Entire Function
• Functional equations and harmonic extensions
• Harmonic Polynomials and Dirichlet-Type Problems
• The Level Curves of Harmonic Functions

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