Non-linear ground state representations and sharp Hardy inequalities
Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.
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Author
Frank, Rupert L;
Seiringer, RobertISTA 
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
Publisher
Academic Press
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. Academic Press. 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. Academic Press, 2008. 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. Academic Press, 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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