Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion
نویسنده
چکیده
In the euclidean space, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. In this paper, we investigate how to relate these inequalities using the flow of a fast diffusion equation in dimension d ≥ 3. The main consequence is an improvement of Sobolev’s inequality when d ≥ 5, which involves the various terms of the dual Hardy-Littlewood-Sobolev inequality. In dimension d = 2, Onofri’s inequality plays the role of Sobolev’s inequality and can also be related to its dual inequality, the logarithmic Hardy-Littlewood-Sobolev inequality, by a super-fast diffusion equation.
منابع مشابه
Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.
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