Non-linear ground state representations and sharp Hardy inequalities

R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430.


Journal Article | Published
Author
;
Abstract
We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.
Publishing Year
Date Published
2008-12-15
Journal Title
Journal of Functional Analysis
Volume
255
Issue
12
Page
3407 - 3430
IST-REx-ID

Cite this

Frank R, Seiringer R. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 2008;255(12):3407-3430. doi:10.1016/j.jfa.2008.05.015
Frank, R., & Seiringer, R. (2008). Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis, 255(12), 3407–3430. https://doi.org/10.1016/j.jfa.2008.05.015
Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” Journal of Functional Analysis 255, no. 12 (2008): 3407–30. https://doi.org/10.1016/j.jfa.2008.05.015.
R. Frank and R. Seiringer, “Non-linear ground state representations and sharp Hardy inequalities,” Journal of Functional Analysis, vol. 255, no. 12, pp. 3407–3430, 2008.
Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.
Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” Journal of Functional Analysis, vol. 255, no. 12, Academic Press, 2008, pp. 3407–30, doi:10.1016/j.jfa.2008.05.015.

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