Harnack inequality and asymptotic lower bounds for the relativistic Fokker-Planck operator

Autor:	Anceschi, Francesca, Polidoro, Sergio, Rebucci, Annalaura
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs 35K70 35Q75 35Q84 35A08
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
Externí odkaz:	http://arxiv.org/abs/2211.05736 Zobrazit plný text záznamu View this record from Arxiv