Harmonic Dirichlet problem for some equilateral triangle

DOI10.1080/17476933.2011.598932zbMath1238.31004OpenAlexW2060024219MaRDI QIDQ3119093

Heinrich Begehr, Tatyana Vaitekhovich

Publication date: 7 March 2012

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2011.598932

zbMATH Keywords

Dirichlet problemequilateral trianglePoisson equationGreen function

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Boundary value problems in the complex plane (30E25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary value and inverse problems for harmonic functions in two dimensions (31A25) Green's functions for elliptic equations (35J08)

Related Items (18)

COMPLEX BOUNDARY VALUE PROBLEMS FOR THE CAUCHY–RIEMANN OPERATOR ON A TRIANGLE ⋮ Dirichlet and Neumann problems for Poisson equation in half Lens ⋮ Schwarz boundary problem on a triangle ⋮ Dirichlet problem for complex Poisson equation in a half hexagon domain ⋮ Integral Representations Related to Complex Partial Differential Operators ⋮ Integral representations in the complex plane and iterated boundary value problems ⋮ Green function for a hyperbolic strip and a class of related plane domains ⋮ Riemann-Hilbert-type boundary value problems on a half hexagon ⋮ Boundary Value Problems and Method of Reflection for Quarter Ring and Half Hexagon ⋮ The Parqueting-Reflection Principle ⋮ Schwarz boundary value problem for the Cauchy-Riemann equation in a rectangle ⋮ Riemann–Hilbert Problems for Monogenic Functions on Upper Half Ball of $${\mathbb {R}}^4$$ R 4 ⋮ SCHWARZ PROBLEM IN LENS AND HALF LENS ⋮ Neumann function for a hyperbolic strip and a class of related plane domains ⋮ A Riemann-Hilbert boundary value problem in a triangle ⋮ Schwarz problem in lens and lune ⋮ Dirichlet problems in lens and lune ⋮ A Riemann-Hilbert boundary value problem in a bounded sector

Uses Software

• SC Toolbox

Cites Work

• Eigenstructure of the equilateral triangle. II: The Neumann problem
• Eigenstructure of the equilateral triangle. III: The Robin problem
• Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem
• Schwarz-Christoffel Mapping

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