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arXiv · 1101.2545

Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients

Gerassimos Barbatis·Pier Domenico Lamberti
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Abstract

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $Ω$ in ${\mathbb{R}}^N$. We consider deformations $ϕ(Ω)$ of $Ω$ obtained by means of a locally Lipschitz homeomorphism $ϕ$ and we estimate the variation of the eigenfunctions and eigenvalues upon variation of $ϕ$. We prove general stability estimates without using uniform upper bounds for the gradients of the maps $ϕ$. As an application, we obtain estimates on the rate of convergence for eigenvalues and eigenfunctions when a domain with an outward cusp is approximated by a sequence of Lipschitz domains.

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Gerassimos Barbatis, Pier Domenico Lamberti. 2011-01-13. Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients. https://doi.org/10.1112/s0025579311002397

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