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.

N1 - Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

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 -