Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591449 | Journal of Functional Analysis | 2010 | 20 Pages |
Abstract
We consider the Laplace operator with Dirichlet boundary conditions on a domain in Rd and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This generalizes our previous results in two dimensions and, as in that case, allows us to obtain an approximation for Dirichlet eigenvalues for a large class of domains, under very mild assumptions. As an application, we derive a three-term asymptotic expansion for the first eigenvalue of d-dimensional ellipsoids.
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