Lieb-Thirring inequalities for higher order differential operators
2008 (English)In: Mathematische Nachrichten, ISSN 0025-584X, Vol. 281, no 2, 199-213 p.Article in journal (Refereed) Published
We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 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 gamma=1-1/(2l) in dimension d=1 with l >= 2 we prove the inequality L-l,r,d(o) < L-l,L-r,L-d, which holds in contrast to current conjectures.
Place, publisher, year, edition, pages
2008. Vol. 281, no 2, 199-213 p.
mathematical physics, spectral theory
IdentifiersURN: urn:nbn:se:uu:diva-112401DOI: 10.1002/mana.200510595ISI: 000253379400004OAI: oai:DiVA.org:uu-112401DiVA: diva2:286159