数学杂志2021，Vol.41Issue(3)：205-211,7.
H(o)rmander向量场型积分泛函的极小元的可积性和有界性
INTEGRABILITY AND BOUNDEDNESS OF MINIMIZERS FOR INTEGRAL FUNCTIONAL OF H(O)RMANDER'S VECTOR FIELDS
摘要
Abstract
The integral functional of H(o)rmander's vector fields is considered,by virtue of the Sobolev inequality related to H(o)rmander's vector fields and the iteration formula of Stampacchia,it is proved that the minimizers of integral functional have higher integrability with the boundary data allowing the higher integrability.Moreover,the L1 (Ω) and L∞ (Ω) boundedness of minimizers are also given,which extends the results of Leonetti and Siepe[12]and Leonetti and Petricca[13]from Euclidean spaces to H(o)rmander's vector fields.关键词
H(o)rmander向量场/积分泛函/极小元/可积性/有界性Key words
H(o)rmander's vector fields/Integral functional/Minimizers/Integrability/Boundedness分类
数理科学引用本文复制引用
冯廷福,张克磊..H(o)rmander向量场型积分泛函的极小元的可积性和有界性[J].数学杂志,2021,41(3):205-211,7.基金项目
Supported by National Natural Science Foundation of China(11701322) （11701322）
Natural Science Foundation of Yunnan Provincial Department of Science and Technology (2019FH001-078) （2019FH001-078）
Natural Science Foundation of Yunnan Provincial Department of Education (2019J0556) （2019J0556）
Natural Science Foundation of Guangxi Provincial Department of Science and Technology (2017GXNSFBA198130). （2017GXNSFBA198130）
