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| 摘要: |
| 本文研究了与微分形式中一类非齐次的Dirac-调和方程解相关的不等式问题.利用非齐次的Dirac-调和方程的条件和Dirac-调和算子D的运算法则，获得了Poincaré不等式，Caccioppoli不等式和弱逆Hölder不等式.作为相关不等式的应用，证明了Poincaré不等式赋特殊权和在Ls（μ）平均域上的形式.本文的研究将齐次Dirac-调和方程解的相关不等式推广到了对应该方程非齐次的情形. |
| 关键词: 非齐次Dirac-调和方程 微分形式 范数不等式 权 Ls(μ)-平均域 |
| DOI： |
| 分类号:O186.15;O175.29 |
| 基金项目:Supported by National Natural Science Foundation of China (11501437); Principal Fund Project of Xi'an Technological University (XAGDXJJ16019). |
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| INEQUALITIES FOR SOLUTIONS OF THE NON-HOMOGENEOUS DIRAC-HARMONIC EQUATIONS IN DIFFERENTIAL FORMS |
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DAI Zhi-min,LIU San-yang
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| Abstract: |
| In this paper, some inequalities related to the solutions of a class of nonhomogeneous Dirac-harmonic equations in differential forms are studied. By the conditions of the Dirac-harmonic equation and the operation rules of Dirac-harmonic operator D, Poincaré inequality, Caccioppoli inequality and the weak inverse Hölder inequality are obtained. As the applications of related inequalities, the forms of the Poincaré inequality with special weights and in the Ls(μ)-averaging domains are proved. The related inequalities of solutions of homogeneous Dirac-harmonic equation are extended to the case of non-homogeneous Dirac-harmonic equation. |
| Key words: Non-homogeneous Dirac-harmonic equations differential forms norm inequalities weights Ls(μ)-averaging domains |
