Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator   in a Domain with Oscillating Boundary. Multiple Eigenvalue Case
  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. 
Youcef Amirat, Gregory A. Chechkin, Rustem R. Gadyl'shin