Translator Disclaimer
2014 Spectral estimates on the sphere
Jean Dolbeault, Maria Esteban, Ari Laptev
Anal. PDE 7(2): 435-460 (2014). DOI: 10.2140/apde.2014.7.435

Abstract

In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the d-dimensional unit sphere. These estimates depend on Lp norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semiclassical asymptotic regime and discuss how our estimates on the sphere differ from those on the Euclidean space.

Citation

Download Citation

Jean Dolbeault. Maria Esteban. Ari Laptev. "Spectral estimates on the sphere." Anal. PDE 7 (2) 435 - 460, 2014. https://doi.org/10.2140/apde.2014.7.435

Information

Received: 7 January 2013; Accepted: 13 June 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1293.35183
MathSciNet: MR3218815
Digital Object Identifier: 10.2140/apde.2014.7.435

Subjects:
Primary: 35P15, 58J50, 81Q10, 81Q35
Secondary: 26D10, 46E35, 47A75, 58E35, 81Q20

Rights: Copyright © 2014 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.7 • No. 2 • 2014
MSP
Back to Top