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Fundamental Solutions to the Laplacian in Plane Domains Bounded by Ellipses

  • H. BegehrEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)

Abstract

Explicit harmonic Robin functions are given for the exterior of an ellipse and for a ring domain bounded by two confocal ellipses of the complex plane. The related Robin problems for the Poisson equation are explicitly solved. As the Robin functions interpolate the Green and Neumann functions the Dirichlet and Neumann problems are by the way treated.

Keywords

Robin, Green and Neumann functions Robin boundary value problem Plane domains bounded by ellipses Doubly connected domain Ring 

Mathematics Subject Classifications:

31A25 31A30 35J08 35J25 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Math. InstitutFU BerlinBerlinGermany

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