Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator

• Autoři: DUONG Giao Ky; FRANK Rupert L.; LE Thi Minh Thao; NAM Phan Thanh; NGUYEN Phuoc-Tai
• Rok publikování: 2024
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal de Mathématiques Pures et Appliquées
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://www.sciencedirect.com/science/article/pii/S0021782424000965
• Doi: http://dx.doi.org/10.1016/j.matpur.2024.103598
• Klíčová slova: Schrödinger operator; Semiclassical estimates; Cwikel-Lieb-Rozenblum inequality; Singular potentials
• Popis: We prove a Cwikel–Lieb–Rozenblum type inequality for the number of negative eigenvalues of the Hardy–Schrödinger operator -?-(d-2)2/(4|x|2)-W(x) on L2(Rd). The bound is given in terms of a weighted Ld/2-norm of W which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian.

Související projekty

• Nonlinear Schrödinger equations and systems with singular potentials