关于微分形式的Caccioppoli-型L^p-和L^φ-积分不等式  

CACCIOPPOLI-TYPE INEQUALITIES WITH L^p-INTEGRATION AND L~φ-INTEGRATION FOR DIFFERENTIAL FORMS

作　　者：李群芳 李华灿[2] LI Qun-fang LI Hua-can(Department of Mathematics, Ganzhou Teachers College, Ganzhou,Jiangxi 341000, China School of Science, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, 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

出　　处：《井冈山大学学报（自然科学版）》2017年第2期12-16,共5页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11461032);江西省教育厅科技项目(GJJ161330,GJJ150646);江西理工大学校级基金项目(NSFJ2015-G25)

摘　　要：微分形式是函数的自然推广,即函数为微分形式的0-形式,目前已成为许多数学分支(如微分几何)研究中的重要工具。本文证明了关于微分形式的A_r^(λ_1/λ_2)(λ_1,λ_2;E)-权Caccioppoli-型L^p-不等式,此不等式可视为许多Caccioppoli-型加权不等式的推广,并给出了相应的Caccioppoli-型L~φ-不等式。Differential form is the natural generalization of the function, which is the differential form with 0- form. Furthermore, it has become an important tool in the study of many branches of mathematics, such as differential geometry. Firstly, we prove the Arλ1/λ2（λ1,λ2;E）- weighted Caccioppoli-type inequality with Lp - integration. It also can be seen as the generalization of many existing weighted Caccioppoli-type inequalities. Furthermore, we give the corresponding Caccioppoli-type inequality with Lφ - integration.

关 键 词：Caccioppoli-型不等式 非齐次A-调和方程 有界域 Jensen's不等式 

分 类 号：O175.2[理学—数学]