Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows
classification
🧮 math.AP
keywords
hardy-littlewood-sobolevdiffusionfastinequalitysharpcasesequationflow
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We give a simple proof of the $\lambda = d-2$ cases of the sharp Hardy-Littlewood-Sobolev inequality for $d\geq 3$, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for $d=2$ via a monotone flow governed by the fast diffusion equation.
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