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

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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.

Original languageEnglish (US)
Pages (from-to)373-383
Number of pages11
JournalMathematical Research Letters
Issue number2-3
StatePublished - 2007

ASJC Scopus subject areas

  • General Mathematics


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