Spectral stability of the p-Laplacian

Burenkov, Victor and Lamberti, Pier Domenico 2009. Spectral stability of the p-Laplacian. Nonlinear Analysis: Theory, Methods & Applications 71 (5-6) , pp. 2227-2235. 10.1016/j.na.2009.01.058

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Abstract

We study the dependence of the eigenvalues of the pp-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 Hölder continuous boundaries, our results improve a result known for the first eigenvalue.

Item Type:	Article
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	pp-Laplacian; Eigenvalues; Domain perturbation
Publisher:	Elsevier
ISSN:	0362-546X
Last Modified:	04 Jun 2017 08:47
URI:	https://orca.cardiff.ac.uk/id/eprint/84903

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