Abstract
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
where \({C^{\mathrm{HR}}_{d,2}}\) is the sharp constant in the Hardy–Rellich inequality and where C γ > 0 is independent of V, is proved for dimensions d = 1, 3. As a corollary of this inequality, a Sobolev-type inequality is obtained.
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Ekholm, T., Enblom, A. Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions. Lett Math Phys 94, 293–312 (2010). https://doi.org/10.1007/s11005-010-0442-0
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DOI: https://doi.org/10.1007/s11005-010-0442-0