Heat equation and the sharp Young's inequality
Mathematical Physics
2012-04-12 v2 Functional Analysis
math.MP
Abstract
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.
Cite
@article{arxiv.1204.2086,
title = {Heat equation and the sharp Young's inequality},
author = {Toscani Giuseppe},
journal= {arXiv preprint arXiv:1204.2086},
year = {2012}
}
Comments
18 pages