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Stability of the Laplace Single Layer Boundary Integral Operator in Sobolev Spaces

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Integral Methods in Science and Engineering, Volume 1

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Abstract

We prove a stability estimate for the Laplace single layer boundary integral operator which generalizes the well known ellipticity estimate to ensure unique solvability of related boundary integral equations.

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Authors and Affiliations

  1. TU Graz, Graz, Austria

    O. Steinbach

Authors
  1. O. Steinbach
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Correspondence to O. Steinbach .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, The University of Tulsa, Tulsa, Oklahoma, USA

    Matteo Dalla Riva

  3. Department of Mathematics, University of Padova, Padova, Italy

    Pier Domenico Lamberti

  4. Systems Analysis, Prognosis and Control, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Paolo Musolino

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Steinbach, O. (2017). Stability of the Laplace Single Layer Boundary Integral Operator in Sobolev Spaces. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_26

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