On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality

On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality

In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an applica...

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Main Authors: G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2011/619623
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spelling doaj-5628f1728c6447f7a67061ec26b5adac2020-11-24T23:21:20ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/619623619623On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type InequalityG. A. Chechkin0Yu. O. Koroleva1L.-E. Persson2P. Wall3Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, RussiaDepartment of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, RussiaNarvik University College, Postboks 385, 8505 Narvik, NorwayDepartment of Engineering Science and Mathematics, Luleå University of Technology, 971 87 Luleå, SwedenIn this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results, the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.http://dx.doi.org/10.1155/2011/619623
collection DOAJ
language English
format Article
sources DOAJ
author G. A. Chechkin
Yu. O. Koroleva
L.-E. Persson
P. Wall
spellingShingle G. A. Chechkin
Yu. O. Koroleva
L.-E. Persson
P. Wall
On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
International Journal of Differential Equations
author_facet G. A. Chechkin
Yu. O. Koroleva
L.-E. Persson
P. Wall
author_sort G. A. Chechkin
title On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
title_short On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
title_full On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
title_fullStr On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
title_full_unstemmed On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
title_sort on spectrum of the laplacian in a circle perforated along the boundary: application to a friedrichs-type inequality
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2011-01-01
description In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results, the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.
url http://dx.doi.org/10.1155/2011/619623
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AT yuokoroleva onspectrumofthelaplacianinacircleperforatedalongtheboundaryapplicationtoafriedrichstypeinequality
AT lepersson onspectrumofthelaplacianinacircleperforatedalongtheboundaryapplicationtoafriedrichstypeinequality
AT pwall onspectrumofthelaplacianinacircleperforatedalongtheboundaryapplicationtoafriedrichstypeinequality
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