Letters in Mathematical Physics

, Volume 105, Issue 7, pp 939–958 | Cite as

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.

Mathematics Subject Classification

Primary: 35R45 81Q10 Secondary: 35J10 58J50 78A50 

Keywords

quantum waveguides twisted tubes Dirichlet Laplacian Hardy inequality 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Philippe Briet
    • 1
    • 2
  • Hiba Hammedi
    • 1
    • 2
  • David Krejčiřík
    • 3
  1. 1.Aix-Marseille Université, CNRS, CPT, UMR 7332, Case 907MarseilleFrance
  2. 2.Université de Toulon, CNRS, CPT, UMR 7332La GardeFrance
  3. 3.Department of Theoretical PhysicsNuclear Physics Institute ASCRŘežCzech Republic

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