Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field
Analysis of PDEs
2020-11-02 v1 Mathematical Physics
Functional Analysis
math.MP
Operator Algebras
Spectral Theory
Abstract
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.
Cite
@article{arxiv.2010.16175,
title = {Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field},
author = {Bernard Helffer and Zeinab Karaki},
journal= {arXiv preprint arXiv:2010.16175},
year = {2020}
}