On the solution of the Dirichlet problem with rational holomorphic boundary data

DOI10.1007/BF03321109zbMath1094.30045OpenAlexW2074322871MaRDI QIDQ2492091

Peter Ebenfelt, Michael Viscardi

Publication date: 6 June 2006

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321109

zbMATH Keywords

Dirichlet problemBergman kernelrational solutionRiemann mapping

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Boundary value problems in the complex plane (30E25)

Related Items

Algebraicity in the Dirichlet problem in the plane with rational data ⋮ 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 ⋮ An explicit solution to the Dirichlet problem with rational holomorphic data in terms of a Riemann mapping ⋮ Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions ⋮ On the classical Dirichlet problem in the plane with rational data

Cites Work

• On the classical Dirichlet problem in the plane with rational data
• Simplicity of the Bergman, Szegö and Poisson kernel functions
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• Dirichlet's Problem When the Data is an Entire Function
• The Dirichlet problem on quadratic surfaces
• Polynomial solutions to Dirichlet problems
• Harmonic Polynomials and Dirichlet-Type Problems
• Complexity of the classical kernel functions of potential theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item