Location of the nodal set for thin curved tubes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F08%3A00311171" target="_blank" >RIV/61389005:_____/08:00311171 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Location of the nodal set for thin curved tubes

Original language description

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 thefirst 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.

Czech name

Lokalisace nodalni mnoziny pro tenke krive trubice

Czech description

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.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2008

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Indiana University Mathematics Journal

ISSN

0022-2518

e-ISSN

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Volume of the periodical

57

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

33

Pages from-to

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UT code for WoS article

000254468900010

EID of the result in the Scopus database

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