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

By Fengbo Hang. 2007

65 citations recorded by the source corpus.

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, we resolve all the cases left open by previous works of Chen, Li and Ou on the corresponding integral systems.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f08e593b5103c6340afa64790c0d0407c23d41b3

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In Applied Mathematics

1. Congming LI #
2. Wenxiong CHEN *
3. Li Ma
4. Yutian Lei
5. Fengbo Hang
6. Dezhong Chen
7. G. Lu
8. Xiaohui Yu

In Computational Theory and Mathematics

1. Congming LI #
2. Wenxiong CHEN *
3. Leyun Wu

Citations in the corpus

• Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, methodology): “There are many more applications of this method to integral systems, and the interested readers may see [10] [12] [15] [20] [21] [28] [33] [34] [40] [42] [45] [46] [47] [50] [53] [54] and the references therein.”
• Sharp criteria of Liouville type for some nonlinear systems (2013, unknown): “[18] and [20]).”