The basic elliptic equations in an equilateral triangle

DOI10.1098/rspa.2005.1466zbMath1186.35040arXivmath/0412031OpenAlexW3103813943MaRDI QIDQ5427643

George Dassios, Athanassios S. Fokas

Publication date: 21 November 2007

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412031

zbMATH Keywords

eigenfunctionselliptic equationsequilateral triangleboundary-value problemsDirichletNeumann

Mathematics Subject Classification ID

Series solutions to PDEs (35C10) Second-order elliptic equations (35J15)

Related Items (15)

On the rigorous foundations of the Fokas method for linear elliptic partial differential equations ⋮ Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle ⋮ Fourier-Mellin transforms for circular domains ⋮ Boundary value problems for the elliptic sine-Gordon equation in a semi-strip ⋮ The Unified Transform and the Water Wave Problem ⋮ The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation ⋮ On the Global Relation and the Dirichlet-to-Neumann Correspondence ⋮ Orthogonality of Bethe ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove ⋮ A new transform method II: the global relation and boundary-value problems in polar coordinates ⋮ Eigenvalues for the Laplace operator in the interior of an equilateral triangle ⋮ Analytic solution of an exterior Neumann problem in a non-convex domain ⋮ Laplace’s equation in the exterior of a convex polygon. The equilateral triangle ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains ⋮ The Poisson and the Biharmonic Equations in the Interior of a Convex Polygon ⋮ The Kelvin transformation as a tool for analyzing problems in medicine and technology

Cites Work

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• A unified transform method for solving linear and certain nonlinear PDEs
• Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem
• On a transform method for the Laplace equation in a polygon
• Explicit integral solutions for the plane elastostatic semi-strip
• The modified Helmholtz equation in a semi-strip

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