Lyapunov functionals for the heat equation and sharp inequalities
The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [...
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| Format: | Article |
| Language: | English |
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Accademia Peloritana dei Pericolanti
2013-01-01
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| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: | http://dx.doi.org/10.1478/AAPP.91S1A18 |
| Summary: | The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [20] 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. |
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| ISSN: | 0365-0359 1825-1242 |