MAXIMAL ESTIMATES FOR THE KRAMERS-FOKKER-PLANCK OPERATOR WITH ELECTROMAGNETIC FIELD

被引：0
|
作者：
Helffer, Bernard [1 ]
Karaki, Zeinab [1 ]
机构：
[1] Univ Nantes, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 3, France
来源：
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 2022年 / 150卷 / 01期
关键词：
Fokker-Planck equation; magnetic field; electric potential; Lie algebra; irreducible representation; maximal estimate;
D O I：
10.24033/bsmf.2842
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1 / 16
页数：16
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