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Hardy Inequalities in Globally Twisted Waveguides

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Abstract

We establish various Hardy-type inequalities for the Dirichlet Laplacian in perturbed periodically twisted tubes of non-circular cross-sections. We also state conjectures about the existence of such inequalities in more general regimes, which we support by heuristic and numerical arguments.

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Authors and Affiliations

  1. Aix-Marseille Université, CNRS, CPT, UMR 7332, Case 907, 13288, Marseille, France

    Philippe Briet & Hiba Hammedi

  2. Université de Toulon, CNRS, CPT, UMR 7332, 83957, La Garde, France

    Philippe Briet & Hiba Hammedi

  3. Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068, Řež, Czech Republic

    David Krejčiřík

Authors
  1. Philippe Briet
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  2. Hiba Hammedi
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  3. David Krejčiřík
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Correspondence to David Krejčiřík.

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Briet, P., Hammedi, H. & Krejčiřík, D. Hardy Inequalities in Globally Twisted Waveguides. Lett Math Phys 105, 939–958 (2015). https://doi.org/10.1007/s11005-015-0768-8

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  • DOI: https://doi.org/10.1007/s11005-015-0768-8

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