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Fundamental Solutions to the Laplacian in Plane Domains Bounded by Ellipses

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Mathematics and Computing (ICMC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

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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.

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Author information

Authors and Affiliations

  1. Math. Institut, FU Berlin, Arnimallee 3, 14195, Berlin, Germany

    H. Begehr

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  1. H. Begehr
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Correspondence to H. Begehr .

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Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Begehr, H. (2017). Fundamental Solutions to the Laplacian in Plane Domains Bounded by Ellipses. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_25

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_25

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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