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Lieb–Thirring inequalities for higher order differential operators

✍ Scribed by Clemens Förster; Jörgen Östensson

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
201 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We derive Lieb–Thirring inequalities for the Riesz means of eigenvalues of order γ ≥ 3/4 for a fourth order operator in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators, in dimensions greater than one. For the critical case γ = 1 – 1/(2__l__) in dimension d = 1 with l ≥ 2 we prove the inequality L^0^~l,γ,d~ < L~l,γ,d~ , which holds in contrast to current conjectures. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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