Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 255, Issue 12, Pages 3407-3430Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2008.05.015
Keywords
Hardy inequality; Sobolev embedding; Ground state substitution; Fractional Sobolev spaces
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Funding
- DAAD [D/06/49117]
- U.S. National Science Foundation [PHY 06 52356]
- A.P. Sloan Fellowship
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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. (C) 2008 Elsevier Inc. All rights reserved.
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