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On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary. / Nazarov, S.A.; Perez, E.

In: Revista Matematica Complutense, Vol. 31, No. 1, 01.01.2018, p. 1-62.

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Harvard

Nazarov, SA & Perez, E 2018, 'On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary', Revista Matematica Complutense, vol. 31, no. 1, pp. 1-62. https://doi.org/10.1007/s13163-017-0243-4

APA

Nazarov, S. A., & Perez, E. (2018). On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary. Revista Matematica Complutense, 31(1), 1-62. https://doi.org/10.1007/s13163-017-0243-4

Vancouver

Nazarov SA, Perez E. On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary. Revista Matematica Complutense. 2018 Jan 1;31(1):1-62. https://doi.org/10.1007/s13163-017-0243-4

Author

Nazarov, S.A. ; Perez, E. / On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary. In: Revista Matematica Complutense. 2018 ; Vol. 31, No. 1. pp. 1-62.

BibTeX

@article{7b79a81d839448238666e90a9b06a66b,
title = "On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary",
abstract = "We construct two-term asymptotics λkε=εm-2(M+εμk+O(ε3/2)) of eigenvalues of a mixed boundary-value problem in Ω ⊂ R 2 with many heavy (m> 2) concentrated masses near a straight part Γ of the boundary ∂Ω. ε is a small positive parameter related to size and periodicity of the masses; k∈ N. The main term M> 0 is common for all eigenvalues but the correction terms μ k, which are eigenvalues of a limit problem with the spectral Steklov boundary conditions on Γ , exhibit the effect of asymptotic splitting in the eigenvalue sequence enabling the detection of asymptotic forms of eigenfunctions. The justification scheme implies isolating and purifying singularities of eigenfunctions and leads to a new spectral problem in weighed spaces with a “strongly” singular weight. ",
keywords = "Asymptotic splitting of eigenvalues, Concentrated masses, Corner singularities, Homogenization problems, Spectral analysis, Steklov problem",
author = "S.A. Nazarov and E. Perez",
note = "Funding Information: Acknowledgements This research work has been partially supported by Spanish MINECO, MTM2013-44883-P. Also, the research work of the first author has been partially supported by Russian Foundation of Basic research (Project 15–01–02175).",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/s13163-017-0243-4",
language = "English",
volume = "31",
pages = "1--62",
journal = "Revista Matematica Complutense",
issn = "1139-1138",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary

AU - Nazarov, S.A.

AU - Perez, E.

N1 - Funding Information: Acknowledgements This research work has been partially supported by Spanish MINECO, MTM2013-44883-P. Also, the research work of the first author has been partially supported by Russian Foundation of Basic research (Project 15–01–02175).

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We construct two-term asymptotics λkε=εm-2(M+εμk+O(ε3/2)) of eigenvalues of a mixed boundary-value problem in Ω ⊂ R 2 with many heavy (m> 2) concentrated masses near a straight part Γ of the boundary ∂Ω. ε is a small positive parameter related to size and periodicity of the masses; k∈ N. The main term M> 0 is common for all eigenvalues but the correction terms μ k, which are eigenvalues of a limit problem with the spectral Steklov boundary conditions on Γ , exhibit the effect of asymptotic splitting in the eigenvalue sequence enabling the detection of asymptotic forms of eigenfunctions. The justification scheme implies isolating and purifying singularities of eigenfunctions and leads to a new spectral problem in weighed spaces with a “strongly” singular weight.

AB - We construct two-term asymptotics λkε=εm-2(M+εμk+O(ε3/2)) of eigenvalues of a mixed boundary-value problem in Ω ⊂ R 2 with many heavy (m> 2) concentrated masses near a straight part Γ of the boundary ∂Ω. ε is a small positive parameter related to size and periodicity of the masses; k∈ N. The main term M> 0 is common for all eigenvalues but the correction terms μ k, which are eigenvalues of a limit problem with the spectral Steklov boundary conditions on Γ , exhibit the effect of asymptotic splitting in the eigenvalue sequence enabling the detection of asymptotic forms of eigenfunctions. The justification scheme implies isolating and purifying singularities of eigenfunctions and leads to a new spectral problem in weighed spaces with a “strongly” singular weight.

KW - Asymptotic splitting of eigenvalues

KW - Concentrated masses

KW - Corner singularities

KW - Homogenization problems

KW - Spectral analysis

KW - Steklov problem

UR - http://www.scopus.com/inward/record.url?scp=85028768128&partnerID=8YFLogxK

U2 - 10.1007/s13163-017-0243-4

DO - 10.1007/s13163-017-0243-4

M3 - Article

VL - 31

SP - 1

EP - 62

JO - Revista Matematica Complutense

JF - Revista Matematica Complutense

SN - 1139-1138

IS - 1

ER -

ID: 35201357