A new proof of the Hardy–Rellich inequality in any dimension

• Published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 150; no. 6; pp. 2894 - 2904
• Main Author: Cazacu, Cristian
• Format: Journal Article
• Language: English
• Published: Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.12.2020; Cambridge University Press
• Subjects: Broken symmetry; Inequality; Spherical harmonics; Hardy inequality; spherical coordinates; 26D10; 35A23

The Hardy-Rellich inequality in the whole space with the best constant was firstly proved by Tertikas and Zographopoulos in Adv. Math. (2007) in higher dimensions N ⩾ 5. Then it was extended to lower dimensions N ∈ {3, 4} by Beckner in Forum Math. (2008) and Ghoussoub-Moradifam in Math. Ann. (2011)...