Giao Ky Duong , Rupert L. Frank , Thi Minh Thao Le , Phan Thành Nam , Phuoc-Tai Nguyen
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引用次数: 0
摘要
我们证明了哈代-薛定谔算子-Δ-(d-2)2/(4|x|2)-W(x) 在 L2(Rd) 上负特征值数量的 Cwikel-Lieb-Rozenblum 型不等式。该约束是通过 W 的加权 Ld/2 准则给出的，在大耦合和小耦合情况下都很尖锐。我们还得到了分数拉普拉卡方的类似约束。
Cwikel–Lieb–Rozenblum type inequalities for Hardy–Schrödinger operator
We prove a Cwikel–Lieb–Rozenblum type inequality for the number of negative eigenvalues of the Hardy–Schrödinger operator on . The bound is given in terms of a weighted -norm of W which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian.
期刊介绍：
Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.
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