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References (30)
-
S. Nazarov (1999)
The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributesRussian Mathematical Surveys, 54
-
V. Maz'ya, S. Nazarov, B. Plamenevskii, Izvestiya Rossiiskoi, Akademii Nauk, Seriya Matematicheskaya (1985)
ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLESMathematics of The Ussr-izvestiya, 24
-
R.R. Gadyl’shin (1996)
On the disturbance of the spectrum of the Laplacian under a change in the type of the boundary condition on a small part of the boundaryComput. Math. Math. Phys., 36
-
(1973)
Kraevye zadachi matematicheskoi fiziki (Boundary Value Problems of -
(1957)
Regular degeneracy and boundary layer for linear differential equations with a small parameter -
V. Maz'ya, S. Nazarov (1989)
Singularities of solutions of the Neumann problem at a conical pointSiberian Mathematical Journal, 30
-
R. Gadyl'shin (1992)
Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary conditionMathematical Notes, 52
-
(1986)
Asymptotics of the eigenvalue of a singularly perturbed self-adjoint elliptic problem with a small parameter in the boundary conditions, Differ -
(1962)
Translated under the title: Izoperimetricheskie neravenstva v matematicheskoi fizike -
(1988)
Mekhanika deformiruemogo tverdogo tela (Mechanics of Deformable Solids) -
S. Hutton (1965)
The Gulf Stream: A Physical and Dynamical Description. By HENRY STOMMEL. Second edition. 248 pp. $6.00.Journal of Fluid Mechanics, 23
-
R. Gadyl'shin (1996)
Perturbation of the Laplacian spectrum when there is a change in the type of boundary condition on a small part of the boundaryComputational Mathematics and Mathematical Physics, 36
-
(1991)
Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten -
(1963)
Boundary value problems for elliptic equations in domains with conical or corner points, Tr -
R.R. Gadyl’shin (1986)
Asymptotics of the eigenvalue of a singularly perturbed self-adjoint elliptic problem with a small parameter in the boundary conditionsDiffer. Uravn., 22
-
S. Nazarov, Boris Plamenevsky (1994)
Elliptic Problems in Domains with Piecewise Smooth Boundaries -
V. Kozlov, V. Maz'ya, J. Roßmann (2002)
Elliptic boundary value problems in smooth domains -
V. Kozlov, V. Maz'ya, J. Roßmann (2002)
Elliptic Boundary Value Problems in Domains with Point Singularities, 52
-
V. Kozlov, Vladimir Maz´ya, A. Movchan (1999)
Asymptotic Analysis of Fields in Multi-Structures -
A. Delitsyn, D.S Grebenkov (2018)
Mode matching methods for spectral and scattering problemsQ. J. Mech. Appl. Math., 71
-
V.G. Maz’ya, B.A. Plamenevskii (1977)
On the coefficients in the asymptotics of solutions to elliptic boundary value problems in a domain with conical pointsMath. Nachr., 76
-
V.A. Kondrat’ev (1963)
Boundary value problems for elliptic equations in domains with conical or corner pointsTr. Mosk. Mat. O-va, 16
-
A. Delitsyn, D. Grebenkov, D. Grebenkov (2017)
Mode matching methods for spectral and scattering problemsThe Quarterly Journal of Mechanics and Applied Mathematics
-
(1976)
Mekhanika sploshnoi sredy -
M.I. Vishik, L.A. Lyusternik (1957)
Regular degeneracy and boundary layer for linear differential equations with a small parameterUsp. Mat. Nauk, 12
-
(1977)
On the coefficients in the asymptotics of solutions to elliptic boundary value problems in a domain with conical points -
(1980)
Spektral'naya teoriya samosopryazhennykh operatorov v gil'bertovom prostranstve (Spectral Theory of Self-adjoint Operators in a Hilbert Space -
G. Pólya, G. Szegő (1951)
Isoperimetric inequalities in mathematical physics -
(1966)
Osnovy sovremennoi teorii potentsiala (Fundamentals of Modern Potential Theory) -
(1989)
Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach (Matching of Asymptotic Expansions of Solutions of Boundary Value Problems)
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/s0012266121060045
- Publisher site
- See Article on Publisher Site
Abstract
We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problemsfor the Laplace operator in a domain separated by several partitions with holes of small diametersand splitting into several independent cells in the limit as the diameters tend to zero. Usingasymptotic methods for singularly perturbed domains, we study the splitting of a multipleeigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundaryconditions, and the localization of the eigenfunction in the case of a simple eigenvalue.
Journal
Differential Equations – Springer Journals
Published: Jul 8, 2021