SPECTRA OF THE DIRICHLET LAPLACIAN IN 3-DIMENSIONAL POLYHEDRAL LAYERS

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SPECTRA OF THE DIRICHLET LAPLACIAN IN 3-DIMENSIONAL POLYHEDRAL LAYERS. / Bakharev, F.L.; Matveenko, S.G.

In: St. Petersburg Mathematical Journal, Vol. 35, No. 4, 2024, p. 597-610.

Research output: Contribution to journal › Article › peer-review

Author

Bakharev, F.L. ; Matveenko, S.G. / SPECTRA OF THE DIRICHLET LAPLACIAN IN 3-DIMENSIONAL POLYHEDRAL LAYERS. In: St. Petersburg Mathematical Journal. 2024 ; Vol. 35, No. 4. pp. 597-610.

BibTeX

@article{3a9734ab27a24ebdaf715b9141924b56,

title = "SPECTRA OF THE DIRICHLET LAPLACIAN IN 3-DIMENSIONAL POLYHEDRAL LAYERS",

abstract = "The structure of the spectrum of the three-dimensional Dirichlet Laplacian in a 3D polyhedral layer of fixed width is studied. It turns out that the essential spectrum is determined by the smallest dihedral angle that forms the boundary of the layer while the discrete spectrum is always finite. An example of a layer with empty discrete spectrum is constructed. The spectrum is proved to be nonempty in regular polyhedral layer. {\textcopyright} 2024 American Mathematical Society",

keywords = "continuous spectrum, Dirichlet layers, discrete spectrum, Laplace operator",

author = "F.L. Bakharev and S.G. Matveenko",

note = "Export Date: 4 November 2024",

year = "2024",

doi = "10.1090/spmj/1818",

language = "Английский",

volume = "35",

pages = "597--610",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "4",

}

RIS

TY - JOUR

T1 - SPECTRA OF THE DIRICHLET LAPLACIAN IN 3-DIMENSIONAL POLYHEDRAL LAYERS

AU - Bakharev, F.L.

AU - Matveenko, S.G.

N1 - Export Date: 4 November 2024

PY - 2024

Y1 - 2024

N2 - The structure of the spectrum of the three-dimensional Dirichlet Laplacian in a 3D polyhedral layer of fixed width is studied. It turns out that the essential spectrum is determined by the smallest dihedral angle that forms the boundary of the layer while the discrete spectrum is always finite. An example of a layer with empty discrete spectrum is constructed. The spectrum is proved to be nonempty in regular polyhedral layer. © 2024 American Mathematical Society

AB - The structure of the spectrum of the three-dimensional Dirichlet Laplacian in a 3D polyhedral layer of fixed width is studied. It turns out that the essential spectrum is determined by the smallest dihedral angle that forms the boundary of the layer while the discrete spectrum is always finite. An example of a layer with empty discrete spectrum is constructed. The spectrum is proved to be nonempty in regular polyhedral layer. © 2024 American Mathematical Society

KW - continuous spectrum

KW - Dirichlet layers

KW - discrete spectrum

KW - Laplace operator

U2 - 10.1090/spmj/1818

DO - 10.1090/spmj/1818

M3 - статья

VL - 35

SP - 597

EP - 610

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 4

ER -

ID: 126740737