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A Hardy inequality in twisted waveguides
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SYSNO ASEP 0311173 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Hardy inequality in twisted waveguides Title Hardyho nerovnost ve zkroucenych vlnovodech Author(s) Ekholm, T. (SE)
Kovařík, Hynek (UJF-V)
Krejčiřík, David (UJF-V) RIDSource Title Archive for Rational Mechanics and Analysis. - : Springer - ISSN 0003-9527
Roč. 188, č. 2 (2008), s. 245-264Number of pages 20 s. Language eng - English Country US - United States Keywords magnetic schrodinger operator ; bound-states ; spectrum Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000254176700003 DOI 10.1007/s00205-007-0106-0 Annotation We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2009
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