Hardy inequalities in globally twisted waveguides

Abstract

We establish various Hardy-type inequalities for the Dirichlet Laplacian in perturbed periodically twisted tubes of non-circular cross-sections. We also state conjectures about the existence of such inequalities in more general regimes, which we support by heuristic and numerical arguments.

18 pages, 1 figure

References in corpus (3)

• A Hardy inequality in twisted waveguides
• Spectrum of the Schrödinger operator in a perturbed periodically twisted tube
• Twisting versus bending in quantum waveguides