Geometric versus Spectral Convergence for the Neumann Laplacian under Exterior Perturbations of the Domain
نویسنده
چکیده
Abstract. We analyze the behavior of the eigenvalues and eigenfunctions of the Laplace operator with homogeneous Neumann boundary conditions when the domain is perturbed. We show that if Ω0 ⊂ Ωǫ are bounded domains (although not necessarily uniformly bounded) and we know that the eigenvalues and eigenfunctions with Neumann boundary condition in Ωǫ converge to the ones in Ω0, then necessarily we have that |Ωǫ \Ω0| → 0 while it is not necessarily true that dist(Ωǫ,Ω0) ǫ→0 −→ 0. As a matter of fact we will construct an example of a perturbation where
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تاریخ انتشار 2009