We consider a class of second-order degenerate kinetic operators L in the framework of special relativity. We first describe L as a Hörmander 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 L f = 0. As a consequence, we obtain a lower bound for the density of the relativistic stochastic process associated with L.
Harnack inequality and asymptotic lower bounds for the relativistic Fokker–Planck operator / Anceschi, F.; Polidoro, S.; Rebucci, A.. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 24:4(2024), pp. 1-28. [10.1007/s00028-024-01021-1]
Harnack inequality and asymptotic lower bounds for the relativistic Fokker–Planck operator
Anceschi F.
Membro del Collaboration Group
;Polidoro S.Membro del Collaboration Group
;Rebucci A.Membro del Collaboration Group
2024
Abstract
We consider a class of second-order degenerate kinetic operators L in the framework of special relativity. We first describe L as a Hörmander 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 L f = 0. As a consequence, we obtain a lower bound for the density of the relativistic stochastic process associated with L.
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