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Villani, Cédric:
Hypocoercive Diffusion Operators
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.2, p. 257-275, Unione Matematica Italiana (english)
pdf (479 Kb), djvu (197 Kb). | MR 2339441 | Zbl 1178.35306

Sunto

In molti problemi provenienti dalla fisica matematica, l'associazione di un operatore di diffusione degenere con un operatore conservativo può portare a dissipazione in tutte le variabili e a convergenza verso l'equilibrio. Si può tracciare un'analogia con il fenomeno ben studiato di ipoellitticità nella teoria della regolarità, ed effettivamente entrambi i fenomeni sono stati studiati insieme. Ora una teoria distinta di ``ipocoercività'' sta iniziando ad emergere con alcuni risultati già sorprendenti e numerosi problemi aperti pieni di sfida. Questo testo (una versione abbreviata di quello che ho preparato per il Congresso Internazionale dei Matematici) ne analizza alcuni.
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