Non-linear ground state representations and sharp Hardy inequalities |
| |
| Authors: | Rupert L. Frank Robert Seiringer |
| |
| Affiliation: | a Department of Mathematics, Princeton University, Washington Road, Princeton, NJ 08544, USA
b Department of Physics, Princeton University, P.O. Box 708, Princeton, NJ 08544, USA |
| |
| 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. |
| |
| Keywords: | Hardy inequality Sobolev embedding Ground state substitution Fractional Sobolev spaces |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
