Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.
We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d≥3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.
Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. carlen@math.rutgers.edu
Eric A
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Carlen
José A
JA
Carrillo
Michael
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