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Counting eigenvalues of biharmonic operators with magnetic fields

✍ Scribed by W. D. Evans; R. T. Lewis

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
226 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

An analysis is given of the spectral properties of perturbations of the magnetic bi‐harmonic operator Δ^2^~A~ in L ^2^(R^n^ ), n = 2, 3, 4, where A is a magnetic vector potential of Aharonov–Bohm type, and bounds for the number of negative eigenvalues are established. Key elements of the proofs are newly derived Rellich inequalities for Δ^2^~A~ which are shown to have a bearing on the limiting cases of embedding theorems for Sobolev spaces H ^2^(R^n^ ). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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