Heat equation and the sharp Young's inequality

Details Heat equation and the sharp Young's inequality Heat equation and the sharp Young's inequality

2012-04-10

arxiv.org/abs/1204.2086v2

Physics

Mathematical Physics

18 pages

Scientific paper

We show that the sharp Young's inequality for convolutions first obtained by Bechner and Brascamp-Lieb can be derived from the monotone in time evolution of a Lyapunov functional of the convolution of two solutions to the heat equation, with different diffusion coefficients, first introduced by Bennett and Bez. Our proof is based on a suitable adaptation of an old idea of Stam and Blachman, used to obtain Shannon's entropy power inequality.

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