Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues
Youcef Amirat, Gregory Aleksandrovich Chechkin, Rustem Rashitovich Gadyl'shin · Applicable Analysis · 2007
We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.