On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs‐Type Inequality
Gregory Aleksandrovich Chechkin, Yulia Koroleva, Lars‐Erik Persson, Peter Wall · International Journal of Differential Equations · 2011
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.