Non-linear ground state representations and sharp Hardy inequalities
Analysis of PDEs
2008-11-15 v2 Mathematical Physics
math.MP
Spectral Theory
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.
Cite
@article{arxiv.0803.0503,
title = {Non-linear ground state representations and sharp Hardy inequalities},
author = {Rupert L. Frank and Robert Seiringer},
journal= {arXiv preprint arXiv:0803.0503},
year = {2008}
}
Comments
AMSLaTeX, 22 pages; extension of the result to the case N<ps