Singular Asymptotic Expansions for Dirichlet Eigenvalues and Eigenfunctions of the Laplacian on Thin Planar Domains
نویسنده
چکیده
We consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We derive the asymptotic expansion for the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This method allows us, for instance, to obtain an approximation for the first Dirichlet eigenvalue for a large class of planar domains, under very mild assumptions.
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