Hörmander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 HÖRMANDER’S VECTOR FIELDS

作　　者：冯廷福 张克磊[2] FENG Ting-fu;ZHANG Ke-lei(School of Mathematics,Kunming University,Kunming,Yunnan,650214;School of Mathematics and Computating Sciences,Guilin University of Electronic Science and Technology,Guilin,Guangxi,541004)

机构地区：[1]昆明学院数学学院,云南昆明650214 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学杂志》2021年第3期205-211,共7页Journal of Mathematics

基　　金：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).

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L^(1)(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.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 L^(1)(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.

关 键 词：Hörmander向量场 积分泛函 极小元 可积性 有界性 

分 类 号：O175.29[理学—数学]