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Journal of Inequalities and Applications
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Hardy inequalities in strips on ruled surfaces

Journal of Inequalities and Applications volume 2006, Article number: 46409 (2006) Cite this article

Abstract

We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and we use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics.

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Authors and Affiliations

  1. Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež, 250 68, Czech Republic

    David Krejčiřík

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  1. David Krejčiřík
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Correspondence to David Krejčiřík.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Krejčiřík, D. Hardy inequalities in strips on ruled surfaces. J Inequal Appl 2006, 46409 (2006). https://doi.org/10.1155/JIA/2006/46409

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  • DOI: https://doi.org/10.1155/JIA/2006/46409

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