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On the Simple Layer Potential Ansatz for the n-Dimensional Helmholtz Equation

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Advances in Microlocal and Time-Frequency Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

In the present paper we consider the Dirichlet problem for the n-dimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of simple layer potentials. The main result concerns the solvability of a boundary integral equation of the first kind. Such a result is here obtained by using the theories of differential forms and reducible operators.

To Prof. Luigi Rodino on occasion of his 70th birthday

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Authors and Affiliations

  1. Department of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

    Alberto Cialdea, Vita Leonessa & Angelica Malaspina

Authors
  1. Alberto Cialdea
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  2. Vita Leonessa
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  3. Angelica Malaspina
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Corresponding author

Correspondence to Angelica Malaspina .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Paolo Boggiatto

  2. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Marco Cappiello

  3. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Elena Cordero

  4. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Sandro Coriasco

  5. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Gianluca Garello

  6. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Alessandro Oliaro

  7. Dipartimento di Matematica "G. Peano", UniversitĂ  degli Studi di Torino, Torino, Italy

    Jörg Seiler

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Cialdea, A., Leonessa, V., Malaspina, A. (2020). On the Simple Layer Potential Ansatz for the n-Dimensional Helmholtz Equation. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_9

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