Počet záznamů: 1  

Location of the nodal set for thin curved tubes

  1. 1.
    0311171 - ÚJF 2009 RIV US eng J - Článek v odborném periodiku
    Freitas, P. - Krejčiřík, David
    Location of the nodal set for thin curved tubes.
    [Lokalisace nodalni mnoziny pro tenke krive trubice.]
    Indiana University Mathematics Journal. Roč. 57, č. 1 (2008), s. 343-375. ISSN 0022-2518. E-ISSN 1943-5258
    Grant CEP: GA MŠMT LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: Dirichlet Laplacian * nodal set * tubes
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 0.810, rok: 2008

    The Dirichlet Laplacian in curved tubes of arbitrary constant cross-section rotating together with the Tang frame along a bounded curve in Euclidean spaces of arbitrary dimension is investigated in the limit when the volume of the cross-section diminishes. We show that spectral properties of the Laplacian are, in this limit, approximated well by those of the sum of the Dirichlet Laplacian in the cross-section and a one-dimensional Schrodinger operator whose potential is expressed solely in terms of the first curvature of the reference curve. In particular, we establish the convergence of eigenvalues, the uniform convergence of eigenfunctions and locate the nodal set of the Dirichlet Laplacian in the tube near nodal points of the one-dimensional Schrodinger operator. As a consequence, we prove the "nodal-line conjecture" for a class of non-convex and possibly multiply connected domains.

    Zabyvame se dirichletovskym laplacianem v krivych trubicich v limite scvrkavajiciho se prurezu. Ukazujeme, ze spektralni vlastnosti laplacianu lze v teto limite aproximovat jednodimensionalnim schroedingerovskym operatorem, jehoz potencial zavisi na krivosti referencni krivky trubice. Jako aplikaci dokazujeme Payneovu "hypotesu o nodalnich carach" pro takovouto tridu nekonvexnich a pripadne i vicesouvislych oblasti.
    Trvalý link: http://hdl.handle.net/11104/0162859

     
     
Počet záznamů: 1  

  Tyto stránky využívají soubory cookies, které usnadňují jejich prohlížení. Další informace o tom jak používáme cookies.