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Lieb–Thirring inequalities for higher order differential operators
Author(s) -
Förster Clemens,
Östensson Jörgen
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510595
Subject(s) - mathematics , differential operator , order (exchange) , dimension (graph theory) , operator (biology) , eigenvalues and eigenvectors , pure mathematics , inequality , differential (mechanical device) , contrast (vision) , mathematical analysis , physics , biochemistry , chemistry , finance , repressor , quantum mechanics , transcription factor , optics , economics , gene , thermodynamics
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)