Non-linear ground state representations and sharp Hardy inequalities

Rupert L. Frank; Robert Seiringer

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arXiv · 0803.0503

Non-linear ground state representations and sharp Hardy inequalities

Rupert L. Frank·Robert Seiringer

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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.

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Rupert L. Frank, Robert Seiringer. 2008-11-14. Non-linear ground state representations and sharp Hardy inequalities. https://arxiv.org/abs/0803.0503

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