Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition

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Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition. / Piat, V. Chiadò; Nazarov, S. A.

In: Journal of Mathematical Sciences (United States), Vol. 251, No. 5, 12.2020, p. 655-695.

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

BibTeX

@article{ae2b22f3d67e4e73b581621599a573b5,

title = "Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition",

abstract = "We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.",

author = "Piat, {V. Chiad{\`o}} and Nazarov, {S. A.}",

year = "2020",

month = dec,

doi = "10.1007/s10958-020-05122-3",

language = "English",

volume = "251",

pages = "655--695",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition

AU - Piat, V. Chiadò

AU - Nazarov, S. A.

PY - 2020/12

Y1 - 2020/12

N2 - We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.

AB - We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.

UR - http://www.scopus.com/inward/record.url?scp=85096001478&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9af3cc2e-ec14-35f0-a56d-7aaa47272e28/

U2 - 10.1007/s10958-020-05122-3

DO - 10.1007/s10958-020-05122-3

M3 - Article

AN - SCOPUS:85096001478

VL - 251

SP - 655

EP - 695

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 71561895