The Dirichlet problem on quadratic surfaces

DOI10.1090/S0025-5718-03-01574-6zbMath1040.31003arXivmath/0212342MaRDI QIDQ4452153

Pamela Gorkin, Sheldon Axler, Karl Voss

Publication date: 12 February 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0212342

zbMATH Keywords

algorithmDirichlet problemLaplace equationlinear equationsquadratic surfaces

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (13)

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 ⋮ The harmonic transvector algebra in two vector variables ⋮ An explicit solution to the Dirichlet problem with rational holomorphic data in terms of a Riemann mapping ⋮ On a mixed Fischer decomposition in Clifford analysis ⋮ 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 Neumann problem on ellipsoids ⋮ The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces ⋮ Dunkl operators and a family of realizations of $\mathfrak{osp}(1\vert2)$ ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Cites Work

• Unnamed Item
• Uniqueness for the \(n\)-dimensional half space Dirichlet problem
• Harmonic Function Theory
• The Dirichlet Problem for Ellipsoids
• An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat Problem
• Dirichlet's Problem When the Data is an Entire Function
• Harmonic Polynomials and Dirichlet-Type Problems

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