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Critical Hardy-Lieb-Thirring Inequalities for Fourth-Order Operators in Low Dimensions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 94, no 3, 293-312 p.Article in journal (Refereed) Published
Abstract [en]

This paper considers Hardy-Lieb-Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality tr((-Delta)(2)-C(d,2)(HR)1/vertical bar x vertical bar(4)-V(x))(-)(gamma)<= C-gamma integral V-Rd(x)(+)(gamma+d/4)dx, gamma >= 1 - d/4, where C-d,2(HR) the sharp constant in the Hardy-Rellich inequality and where C-gamma > 0 is independent of V. is proved for dimensions d = 1, 3. As a corollary of this inequality, a Sobolev-type inequality is obtained.

Place, publisher, year, edition, pages
2010. Vol. 94, no 3, 293-312 p.
Keyword [en]
Hardy-Lieb-Thirring inequalities, fourth-order operators, critical exponents, Sobolev-type inequalities
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-27971DOI: 10.1007/s11005-010-0442-0ISI: 000284975600004Scopus ID: 2-s2.0-78149498565OAI: oai:DiVA.org:kth-27971DiVA: diva2:382853
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098Swedish Research Council
Note
QC 20110103Available from: 2011-01-03 Created: 2011-01-03 Last updated: 2017-12-11Bibliographically approved

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