Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with an oscillating boundary
Youcef Amirat, Gregory Aleksandrovich Chechkin, Rustem Rashitovich Gadyl'shin · Computational Mathematics and Mathematical Physics · 2006
The asymptotic behavior of solutions to spectral problems for the Laplace operator in a domain with a rapidly oscillating boundary is analyzed. The leading terms of the asymptotic expansions for eigenelements are constructed, and the asymptotics are substantiated for simple eigenvalues.