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

  • Alberto Cialdea
  • Vita Leonessa
  • Angelica MalaspinaEmail author
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Part of the Applied and Numerical Harmonic Analysis book series (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.

Keywords

Helmholtz equation Potential theory Integral representations 

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alberto Cialdea
    • 1
  • Vita Leonessa
    • 1
  • Angelica Malaspina
    • 1
    Email author
  1. 1.Department of Mathematics, Computer Science and EconomicsUniversity of BasilicataPotenzaItaly

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