## International Journal of Differential Equations

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

### 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

#### 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