2006/11/01 by Pedro Freitas, David Krejcirik, David Krejčiřı́k · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P15 #msc:58J50 #msc:81Q10
paper · pdf · doi:10.1007/s11040-007-9015-6
published as Math. Phys. Anal. Geom. 9 (2006), no. 4, 335-352. · 20 pages, LaTeX with 1 EPS figure; to appear in Mathematical Physics, Analysis and Geometry
openalex publication_date 2006/11/01 · arxiv created 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet-Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kriz.