Lieb–Thirring inequalities for higher order differential operators |
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| Authors: | Clemens Förster Jörgen Östensson |
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| Institution: | 1. Institute for Analysis, Dynamics and Modelling, Faculty of Mathematics and Physics, University Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;2. Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden |
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| 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Mathematical physics spectral theory |
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