A Hardy inequality in twisted waveguides

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F08%3A00311173" target="_blank" >RIV/61389005:_____/08:00311173 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A Hardy inequality in twisted waveguides
Original language description
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 curvein 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.
Czech name
Hardyho nerovnost ve zkroucenych vlnovodech
Czech description
Ukazujeme, ze zkrouceni nekonecne trubice nekruhoveho prurezu vede k nerovnostem Hardyho typu pro odpovidajici dirichletovsky laplacian. Jako aplikaci dokazeme jistou stabilitu spektra pro laplacian v lokalne zkroucenych a ohnutych trubicich.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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