Počet záznamů: 1

SPECTRUM OF THE LAPLACIAN IN A NARROW CURVED STRIP WITH COMBINED DIRICHLET AND NEUMANN BOUNDARY CONDITIONS

  1. 1.
    0330433 - UJF-V 2010 RIV FR eng J - Článek v odborném periodiku
    Krejčiřík, David
    SPECTRUM OF THE LAPLACIAN IN A NARROW CURVED STRIP WITH COMBINED DIRICHLET AND NEUMANN BOUNDARY CONDITIONS.
    Esaim-Control Optimisation and Calculus of Variations. Roč. 15, č. 3 (2009), s. 555-568 ISSN 1262-3377
    Grant CEP: GA MŠk LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: Laplacian in tubes * Dirichlet and Neumann boundary conditions * dimension reduction
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 1.084, rok: 2009

    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.
    Trvalý link: http://hdl.handle.net/11104/0176222