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Hardy inequalities in tubular domains

GFM seminar
CIUL, amphitheatre
2006-03-31 14:30 .. 15:30
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by David Krejcirik (Department of Theoretical Physics, Nuclear Physics Intitute, Academy of Sciences, Rez, Czech Republic)

We show that twist of an unbounded tube in the Euclidean space gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Laplacian in locally and mildly bent tubes with non-circular cross-section. We also discuss analogous phenomena induced by curvature of an ambient space or by alteration of boundary conditions.
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