Curved nonlinear waveguides

Baldelli, Laura; Krejčiřík, David

doi:10.1016/j.na.2025.113814

1-s2.0-S0362546X25000689-main.pdf (980.6Kb)

Identificadores

URI: https://hdl.handle.net/10481/103798

DOI: 10.1016/j.na.2025.113814

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Editorial

Elsevier

Fecha

2025-09

Referencia bibliográfica

L. Baldelli and D. Krejčiřík. Nonlinear Analysis 258 (2025) 113814. https://doi.org/10.1016/j.na.2025.113814

Patrocinador

Czech Science Foundation EXPRO 20-17749X; Czech Technical University in Prague; National Science Centre, Poland (2020/37/B/ST1/02742); INdAM-GNAMPA Project 2023 (E53C22001930001); MICINN/AEI IMAG-Maria de Maeztu Excellence Grant CEX2020-001105-M

Resumen

The Dirichlet -Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the essential spectrum is positive whenever the cross-section is centrally symmetric and the tube is asymptotically straight, untwisted and non-trivially bent. Second, a Hardy-type inequality is derived for unbent and non-trivially twisted tubes.

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