Heat equation and the sharp Young's inequality [PDF]
Toscani GiuseppeWe 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.View original: http://arxiv.org/abs/1204.2086
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