Fundamental solution of the Laplacian on flat tori and boundary value problems for the planar Poisson equation in rectangles

DOI10.1186/s13661-014-0221-4zbMath1304.35238OpenAlexW2151629800WikidataQ59394249 ScholiaQ59394249MaRDI QIDQ481598

Malik Mamode

Publication date: 12 December 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-014-0221-4

zbMATH Keywords

analytical solutionflat torusboundary value problemhorizonGreen function2D Poisson equation

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Green's functions for elliptic equations (35J08)

Related Items (7)

Integrability of point-vortex dynamics via symplectic reduction: a survey ⋮ Computation of the Madelung constant for hypercubic crystal structures in any dimension ⋮ Analytic dependence of a periodic analog of a fundamental solution upon the periodicity parameters ⋮ Lattice Green/Neumann function for the 2D Laplacian operator defined on square lattice on cylinders, tori and other geometries with some applications ⋮ Harmonic Functions on Finitely Connected Tori ⋮ Mapping properties of weakly singular periodic volume potentials in Roumieu classes ⋮ Atomistic origins of continuum dislocation dynamics

Uses Software

• Schwarz-Christoffel
• SC Toolbox

Cites Work

• Computability of series representations for Green's functions in a rectangle
• The closed-form solution for the 2D Poisson equation with a rectangular boundary
• Miscible porous media displacements in the quarter five-spot configuration. Part 1. The homogeneous case
• Schwarz-Christoffel Mapping
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