关于Hodge-Dirac微分算子的Caccioppoli不等式  

Caccioppoli Inequalities for Hodge-Dirac Differential Operator

作　　者：李群芳 周治廷 邹翠 李华灿[2] LI Qun-fang;ZHOU Zhi-ting;ZOU Cui;LI Hua-can(Department of Mathematics, Ganzhou Teachers College, Ganzhou 341000, China;School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China;Basic Department, Army Infantry College, Nanchang 330000, China)

机构地区：[1]赣州师范高等专科学校数学系,江西赣州341000 [2]江西理工大学理学院,江西赣州341000 [3]陆军步兵学院基础部,江西南昌330000

出　　处：《数学的实践与认识》2018年第8期222-226,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461032);江西省教育厅科技项目(GJJ161330,GJJ150646)

摘　　要：利用广义Hlder不等式、满足Dirac-调和方程的微分形式的弱逆Hlder不等式等重要引理,在已有的关于Hodge-Dirac微分算子的Caccioppoli-型不等式的基础上,首先给出局部的双权Caccioppoli-型积分不等式的参数形式.进一步,作为上述局部结论的应用,在有界域Ω上给出了相应的全局加权积分不等式.结论中的四个参数λ1,λ2,λ3,α使得到的结论更具灵活性,若赋予参数以适当的值可以得到了其它经典权函数的加权积分不等式.Based on the existed Caccioppoli-type inequality of Hodge-Dirac differential operator, in this paper we first give the local parametric version of two weight Caccioppoli-type integral inequality by using some important Lemmas including generalized HSlder inequality and the weak reverse HSlder inequality for differential forms satisfying Dirac-harmonic equation. Furthermore, as application of the above local result, we also prove corresponding global weighted integral inequality on a bounded domain Ω. Four parameters λ1,λ2, λ3, α in conclusions make our conclusions more flexible. If we choose these parameters some proper numerial number, we can obtain some other weighted integral inequalities with some classical weights.

关 键 词：Dirac-调和方程 微分形式 积分不等式 微分算子 

分 类 号：O175.3[理学—数学] O178[理学—基础数学]