A Hardy inequality in twisted waveguides

0311173 - ÚJF 2009 RIV US eng J - Journal Article
Ekholm, T. - Kovařík, Hynek - Krejčiřík, David
A Hardy inequality in twisted waveguides.
[Hardyho nerovnost ve zkroucenych vlnovodech.]
Archive for Rational Mechanics and Analysis. Roč. 188, č. 2 (2008), s. 245-264. ISSN 0003-9527. E-ISSN 1432-0673
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : magnetic schrodinger operator * bound-states * spectrum
Subject RIV: BE - Theoretical Physics
Impact factor: 2.371, year: 2008

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.

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.
Permanent Link: http://hdl.handle.net/11104/0162861