On the Properties of Quasi-periodic Boundary Integral Operators for the Helmholtz Equation

Rubén Aylwin, Carlos Jerez-Hanckes, José Pinto

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the mapping properties of boundary integral operators arising when solving two-dimensional, time-harmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasi-periodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for Rayleigh-Wood frequencies, continuity and coercivity results are derived to prove wellposedness of the associated first kind boundary integral equations.

Original languageEnglish
Article number17
JournalIntegral Equations and Operator Theory
Volume92
Issue number2
DOIs
StatePublished - 1 Apr 2020

Keywords

  • Boundary integral equations
  • Gratings
  • Quasi-periodic functions
  • Wave scattering

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