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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Poincar\'{e}不等式, Caccioppoli不等式 和 弱逆 H\"{o}lder不等式 .作为相关不等式的应用,证明了Poincar\'{e}不等式赋特殊权和在$L^s(\mu)$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 $L^{s}(\mu)$-平均域 |
| DOI： |
| 分类号:O186.15 ; O175.29 |
| 基金项目:广义 Frenkel-Kontorova 模型中的有序结构与无序结构（国家自然科学基金青年项目） |
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| Inequalities for solutions of the non-homogeneous Dirac-harmonic equations in differential forms |
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daizhimin
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| Abstract: |
| In this paper, inequalities related to 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 $D$, Poincar\'{e} inequality, Caccioppoli inequality and the weak inverse H\"{o}lder inequality are obtained. As the applications of related inequalities, the forms of the Poincar\'{e} inequality with special weights and in the $L^{s}(\mu)$-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 $L^{s}(\mu)$-averaging domains |
