Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4604529 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2009 | 14 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis