On the integral systems related to Hardy-Littlewood-Sobolev inequality

Details On the integral systems related to Hardy-Littlewood-Sobolev inequality On the integral systems related to Hardy-Littlewood-Sobolev inequality

2007-03-27

arxiv.org/abs/math/0703778v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality
are smooth. More generally, we show all the nonnegative critical functions are
smooth, radial with respect to some points and strictly decreasing in the
radial direction. In particular, this resolves all the cases left open by
previous works of Chen, Li and Ou on the corresponding integral systems.

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