Hardy inequalities in globally twisted waveguides
Philippe Briet, Hiba Hammedi, David Krejcirik
TL;DR
This paper proves Hardy inequalities for the Dirichlet Laplacian in twisted waveguides with non-circular cross-sections and discusses conjectures for more general cases supported by heuristic and numerical evidence.
Contribution
It establishes Hardy inequalities in periodically twisted tubes and proposes conjectures for broader regimes, supported by heuristic and numerical analysis.
Findings
Hardy inequalities are valid in certain twisted waveguides.
Conjectures are proposed for more general regimes.
Heuristic and numerical evidence supports the conjectures.
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.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations