# Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 3, page 555-568
- ISSN: 1292-8119

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topKrejčiřík, David. "Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2009): 555-568. <http://eudml.org/doc/244858>.

@article{Krejčiřík2009,

abstract = {We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one is the biggest. We also show that the asymptotics can be obtained from a form of norm-resolvent convergence which takes into account the width-dependence of the domain of definition of the operators involved.},

author = {Krejčiřík, David},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {laplacian in tubes; Dirichlet and Neumann boundary conditions; dimension reduction; norm-resolvent convergence; binding effect of curvature; waveguides; Laplacian in tubes},

language = {eng},

number = {3},

pages = {555-568},

publisher = {EDP-Sciences},

title = {Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions},

url = {http://eudml.org/doc/244858},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Krejčiřík, David

TI - Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2009

PB - EDP-Sciences

VL - 15

IS - 3

SP - 555

EP - 568

AB - We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one is the biggest. We also show that the asymptotics can be obtained from a form of norm-resolvent convergence which takes into account the width-dependence of the domain of definition of the operators involved.

LA - eng

KW - laplacian in tubes; Dirichlet and Neumann boundary conditions; dimension reduction; norm-resolvent convergence; binding effect of curvature; waveguides; Laplacian in tubes

UR - http://eudml.org/doc/244858

ER -

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## Citations in EuDML Documents

top- David Krejčiřík, Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
- Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
- Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods

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