The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This maybe not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory and kinetic theory established a useful connection between Boltzmann’s H-functional and Fisher information exactly by means of the solution to the heat equation. In this note, we briefly discuss these original ideas, together with some new application.
Lyapunov functionals for the heat equation and sharp inequalities
TOSCANI, GIUSEPPE
2013-01-01
Abstract
The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This maybe not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory and kinetic theory established a useful connection between Boltzmann’s H-functional and Fisher information exactly by means of the solution to the heat equation. In this note, we briefly discuss these original ideas, together with some new application.File in questo prodotto:
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