We study the dependence of the eigenvalues of the p-Laplacian upon domain perturbation. We prove Lipschitz-type estimates for the deviation of the eigenvalues following a domain perturbation. Such estimates are expressed in terms of suitable measures of vicinity between open sets, such as the 'atlas distance' and the 'lower Hausdorff-Pompeiu deviation'. In the case of open sets with Holder continuous boundaries, our results improve a result known for the first eigenvalue.
Spectral stability of the p-Laplacian
BURENKOV, VICTOR;LAMBERTI, PIER DOMENICO
2009
Abstract
We study the dependence of the eigenvalues of the p-Laplacian upon domain perturbation. We prove Lipschitz-type estimates for the deviation of the eigenvalues following a domain perturbation. Such estimates are expressed in terms of suitable measures of vicinity between open sets, such as the 'atlas distance' and the 'lower Hausdorff-Pompeiu deviation'. In the case of open sets with Holder continuous boundaries, our results improve a result known for the first eigenvalue.
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