International Journal of Differential Equations

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

G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, and P. Wall

Full-text: Open access

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.

Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 619623, 22 pages.

Dates
Received: 24 May 2011
Accepted: 30 August 2011
First available in Project Euclid: 25 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485313257

Digital Object Identifier
doi:10.1155/2011/619623

Mathematical Reviews number (MathSciNet)
MR2854944

Zentralblatt MATH identifier
1239.35106

Citation

Chechkin, G. A.; Koroleva, Yu. O.; Persson, L.-E.; Wall, P. On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality. Int. J. Differ. Equ. 2011 (2011), Article ID 619623, 22 pages. doi:10.1155/2011/619623. https://projecteuclid.org/euclid.ijde/1485313257


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References

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