2007/03/27 by Fengbo Hang, Hang, Fengbo
Computer Science · Mathematics · #35J60 #45G05 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.math/0703778
openalex publication_date 2007/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.