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Hörmander向量场型积分泛函的极小元的可积性和有界性
冯廷福,张克磊
作者单位
冯廷福 昆明学院数学学院, 云南 昆明 650214 
张克磊 桂林电子科技大学数学与计算科学学院, 广西 桂林 541004 
摘要:
本文考虑Hörmander向量场型积分泛函,当边界值具有更高可积性时,借助Hörmander向量场上的Sobolev不等式和Stampacchia的迭代公式证明此积分泛函的极小元也会有更高可积性.此外还得到极小元的L1(Ω)和L(Ω)有界性,从而把Leonetti和Siepe[12]以及Leonetti和Petricca[13]的结果从欧式空间延拓到Hörmander向量场.
关键词:  Hörmander向量场  积分泛函  极小元  可积性  有界性
DOI:
分类号:O175.29
基金项目:Supported by National Natural Science Foundation of China(11701322); Natural Science Foundation of Yunnan Provincial Department of Science and Technology (2019FH001-078); Natural Science Foundation of Yunnan Provincial Department of Education (2019J0556); Natural Science Foundation of Guangxi Provincial Department of Science and Technology (2017GXNSFBA198130).
INTEGRABILITY AND BOUNDEDNESS OF MINIMIZERS FOR INTEGRAL FUNCTIONAL OF HÖRMANDER’S VECTOR FIELDS
FENG Ting-fu,ZHANG Ke-lei
Abstract:
The integral functional of Hörmander’s vector fields is considered, by virtue of the Sobolev inequality related to Hörmander’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 Hörmander’s vector fields.
Key words:  Hörmander’s vector fields  Integral functional  Minimizers  Integrability  Boundedness

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