Lieb–Thirring inequalities for higher order differential operators
- 10 January 2008
- journal article
- research article
- Published by Wiley in Mathematische Nachrichten
- Vol. 281 (2) , 199-213
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/(2l) in dimension d = 1 with l ≥ 2 we prove the inequality L0l,γ,d < Ll,γ,d , which holds in contrast to current conjectures.Keywords
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