| 李群芳,李华灿.关于微分形式的Caccioppoli-型Lp-和Lφ-积分不等式[J].井冈山大学自然版,2017,(2):12-16 |
| 关于微分形式的Caccioppoli-型Lp-和Lφ-积分不等式 |
| CACCIOPPOLI-TYPE INEQUALITIES WITH LP-INTEGRATION AND Lφ-INTEGRATION FOR DIFFERENTIAL FORMS |
| 投稿时间：2016-07-06 修订日期：2016-08-28 |
| DOI：10.3969/j.issn.1674-8085.2017.02.003 |
| 中文关键词: Caccioppoli-型不等式 非齐次A-调和方程 有界域 Jensen's不等式 |
| 英文关键词: Caccioppoli-type inequality nonhomogeneous A-harmonic equation bounded domain Jensen's inequality |
| 基金项目: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） |
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| 中文摘要: |
| 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Arλ1/λ2（λ1，λ2；E）权Caccioppoli-型Lp-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Lφ-不等式。 |
| 英文摘要: |
| Differential form is the natural generalization of the function, which is the differential form with 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 Lφ-inequalities. Furthermore, we give the corresponding Caccioppoli-type inequality with integration. |
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