Abstract
Consider the Dirichlet Laplacian operator \(-\Delta ^D\) in a periodic waveguide \(\Omega \). Under the condition that \(\Omega \) is sufficiently thin, we show that its spectrum \(\sigma (-\Delta ^D)\) is absolutely continuous (in each finite region). In addition, we ensure the existence of at least one gap in \(\sigma (-\Delta ^D)\) and locate it.
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Acknowledgements
The authors would like to thank Dr. César R. de Oliveira and Dr. David Krejčířik for useful discussions.
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C. R. Mamani: Supported by CAPES.
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Mamani, C.R., Verri, A.A. Absolute Continuity and Band Gaps of the Spectrum of the Dirichlet Laplacian in Periodic Waveguides. Bull Braz Math Soc, New Series 49, 495–513 (2018). https://doi.org/10.1007/s00574-017-0065-5
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DOI: https://doi.org/10.1007/s00574-017-0065-5