Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field

Bernard Helffer (1, 2) , Zeinab Karaki (3, 4)

1 UN UFR ST - Université de Nantes - UFR des Sciences et des Techniques
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 UPVD - Université de Perpignan Via Domitia
4 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

In continuation of a former work by the first author with F. Nier (2009) and of a more recent work by the second author on the torus (2019), we consider the Kramers-Fokker-Planck operator (KFP) with an external electromagnetic field on R d. We show a maximal type estimate on this operator using a nilpotent approach for vector field polynomial operators and induced representations of a nilpotent graded Lie algebra. This estimate leads to an optimal characterization of the domain of the closure of the KFP operator and a criterion for the compactness of the resolvent.

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Algèbres d'opérateurs [math.OA]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Bernard Helffer, Zeinab Karaki. Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field. 2020. ⟨hal-02983476⟩