On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality. (11th August 2011)

• Record Type: Journal Article
• Authors: Chechkin, G. A.; Koroleva, Yu. O.; Persson, L.-E.; Wall, P.
• Other Names: Humi Mayer Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2011(2011)
• Publication Date: 2011-08-11
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2011/619623
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : 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.