Lieb-Thirring inequalities for higher order differential operators

Details Lieb-Thirring inequalities for higher order differential operators Lieb-Thirring inequalities for higher order differential operators

2004-12-16

arxiv.org/abs/math-ph/0412054v1

Physics

Mathematical Physics

18 pages, submitted to Comm. Part. Diff. Eq

Scientific paper

We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schr\"odinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators. For the critical case gamma = 1 - 1/2l in dimension d=1 with differential order 2l >= 4 we prove the strict inequality L^0(l,gamma,d) < L(l,gamma,d), which holds in contrast to current conjectures.

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