Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions

@article{Moiola2019AcousticTP,
  title={Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions},
  author={Andrea Moiola and Euan A. Spence},
  journal={Mathematical Models and Methods in Applied Sciences},
  year={2019}
}
  • A. Moiola, E. Spence
  • Published 2 February 2017
  • Mathematics
  • Mathematical Models and Methods in Applied Sciences
We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds explicit in all parameters. In particular, the (weighted) [Formula: see text] norm of the solution is bounded by the [Formula: see text] norm of the source term, independently of the wavenumber. These bounds then imply the existence of a resonance-free strip… 

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