Extension of the notion of a gap to differential operators defined on different open sets

Burenkov, Victor and Feleqi, Ermal ORCID: https://orcid.org/0000-0002-9661-0684 2013. Extension of the notion of a gap to differential operators defined on different open sets. Mathematische Nachrichten 286 (5-6) , pp. 518-535. 10.1002/mana.201100073

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Abstract

In this paper the notion of a gap between two linear operators is extended to the case of linear differential operators defined on different open sets. Estimates of the gap between second order uniformly elliptic partial differential operators subject to homogeneous Dirichlet boundary conditions defined on different open sets Ω1 and Ω2 are obtained in terms of the geometrical characteristics of vicinity of Ω1 and Ω2. These estimates can be used for obtaining spectral stability estimates for the eigenvalues and eigenfunctions of the aforementioned operators.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Gap between linear operators; elliptic operators;
Publisher:	Wiley
ISSN:	0025-584X
Date of Acceptance:	17 September 2011
Last Modified:	31 Oct 2022 10:26
URI:	https://orca.cardiff.ac.uk/id/eprint/84895

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