Lieb–Thirring inequalities for higher order differential operators
Copyright policy )Lieb–Thirring inequalities for higher order differential operators
AbstractWe 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)
- Uppsala University Sweden
- University of Stuttgart Germany
35P15 (Primary) 47A75, 35J10 (Secondary), General theory of partial differential operators, FOS: Physical sciences, Estimates of eigenvalues in context of PDEs, General topics in linear spectral theory for PDEs, Mathematical Physics (math-ph), Mathematics - Spectral Theory, Sobolev spaces, FOS: Mathematics, polyharmonic operators, Riesz means, Spectral Theory (math.SP), Lieb-Thirring inequalities, negative eigenvalues, Mathematical Physics
35P15 (Primary) 47A75, 35J10 (Secondary), General theory of partial differential operators, FOS: Physical sciences, Estimates of eigenvalues in context of PDEs, General topics in linear spectral theory for PDEs, Mathematical Physics (math-ph), Mathematics - Spectral Theory, Sobolev spaces, FOS: Mathematics, polyharmonic operators, Riesz means, Spectral Theory (math.SP), Lieb-Thirring inequalities, negative eigenvalues, Mathematical Physics
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