Dirichlet's problem and complex lightning bolts

DOI10.1007/BF03321717zbMath1161.30002MaRDI QIDQ2378572

Erik Lundberg

Publication date: 13 January 2009

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

zbMATH Keywords

singularityanalytic continuationalgebraic curvelightning boltalgebraic entire dataapproximation by superpositionsEbenfelt's exampleill-posed problems for the wave equationVekua hull

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Boundary value problems in the complex plane (30E25) Proceedings, conferences, collections, etc. pertaining to functions of a complex variable (30-06)

Related Items (6)

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 Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces ⋮ Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Cites Work

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• On the classical Dirichlet problem in the plane with rational data
• Partial differential equations. 3rd ed
• A boundary value problem for the wave equation
• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• Algebraicity in the Dirichlet problem in the plane with rational data
• The vekua hull of a plane domain
• Dirichlet's Problem When the Data is an Entire Function
• Functional equations and harmonic extensions
• Polynomial solutions to Dirichlet problems

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