Fundamental solution of the Laplacian on flat tori and boundary value problems for the planar Poisson equation in rectangles
| Autor: | Malik Mamode |
|---|---|
| Přispěvatelé: | Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT (PIMENT), Université de La Réunion (UR) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Algebra and Number Theory
Partial differential equation flat torus 2D Poisson equation Mathematical analysis Elliptic function 16. Peace & justice horizon analytical solution Green function [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] boundary value problem Free boundary problem Fundamental solution Method of fundamental solutions Boundary value problem PACS Codes: 02.30.Em 02.30.Jr Poisson's equation Laplace operator Analysis Mathematics |
| Zdroj: | Boundary Value Problems Boundary Value Problems, SpringerOpen, 2014, 2014 (1), pp.221. ⟨10.1186/s13661-014-0221-4⟩ |
| ISSN: | 1687-2762 1687-2770 |
| DOI: | 10.1186/s13661-014-0221-4⟩ |
| Popis: | International audience; The fundamental solution of the Laplacian on flat tori is obtained using Eisenstein's approach to elliptic functions via infinite series over lattices in the complex plane. Most boundary value problems stated for the planar Poisson equation in a rectangle for which series-only representations of solution were known, may thus be solved explicitly in closed-form using the method of images. Moreover, the fundamental solution of n-Laplacian on flat tori may also be simply derived by a convolution power. |
| Databáze: | OpenAIRE |
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