Harnack inequality and asymptotic lower bounds for the relativistic Fokker-Planck operator
Autor: | Anceschi, Francesca, Polidoro, Sergio, Rebucci, Annalaura |
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Rok vydání: | 2022 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We consider a class of second order degenerate kinetic operators $\mathscr{L}$ in the framework of special relativity. We first describe $\mathscr{L}$ as an H\"ormander operator which is invariant with respect to Lorentz transformations. Then we prove a Lorentz-invariant Harnack type inequality, and we derive accurate asymptotic lower bounds for positive solutions to $\mathscr{L} f = 0$. As a consequence we obtain a lower bound for the density of the relativistic stochastic process associated to $\mathscr{L}$. Comment: 23 pages |
Databáze: | arXiv |
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