{"status":"public","publist_id":"4543","type":"journal_article","month":"12","volume":255,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0803.0503"}],"year":"2008","publication":"Journal of Functional Analysis","page":"3407 - 3430","citation":{"ista":"Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430.","ama":"Frank R, Seiringer R. Non-linear ground state representations and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. 2008;255(12):3407-3430. doi:<a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">10.1016/j.jfa.2008.05.015</a>","ieee":"R. Frank and R. Seiringer, “Non-linear ground state representations and sharp Hardy inequalities,” <i>Journal of Functional Analysis</i>, vol. 255, no. 12. Academic Press, pp. 3407–3430, 2008.","mla":"Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>, vol. 255, no. 12, Academic Press, 2008, pp. 3407–30, doi:<a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">10.1016/j.jfa.2008.05.015</a>.","short":"R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430.","chicago":"Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” <i>Journal of Functional Analysis</i>. Academic Press, 2008. <a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">https://doi.org/10.1016/j.jfa.2008.05.015</a>.","apa":"Frank, R., &#38; Seiringer, R. (2008). Non-linear ground state representations and sharp Hardy inequalities. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2008.05.015\">https://doi.org/10.1016/j.jfa.2008.05.015</a>"},"oa":1,"date_published":"2008-12-15T00:00:00Z","issue":"12","date_created":"2018-12-11T11:57:20Z","doi":"10.1016/j.jfa.2008.05.015","title":"Non-linear ground state representations and sharp Hardy inequalities","intvolume":"       255","publisher":"Academic Press","publication_status":"published","day":"15","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer"}],"date_updated":"2021-01-12T06:57:08Z","quality_controlled":0,"extern":1,"_id":"2381","abstract":[{"lang":"eng","text":"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."}]}