微分形式中的非齐次Dirac-调和方程解的若干不等式  

INEQUALITIES FOR SOLUTIONS OF THE NON-HOMOGENEOUS DIRAC-HARMONIC EQUATIONS IN DIFFERENTIAL FORMS

作　　者：戴志敏 刘三阳[1] DAI Zhi-min;LIU San-yang(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China;School of Science,Xi'an Technological University,Xi'an 710021,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710126 [2]西安工业大学理学院,陕西西安710021

出　　处：《数学杂志》2020年第3期267-282,共16页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11501437);Prin-cipal Fund Project of Xi'an Technological University(XAGDXJJ16019).

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Poincare不等式,Caccioppoli不等式和弱逆Holder不等式.作为相关不等式的应用,证明了Poincare不等式赋特殊权和在L^s(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.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,Poincare inequality,Caccioppoli inequality and the weak inverse Holder inequality are obtained.As the applications of related inequalities,the forms of the Poincare inequality with special weights and in the L^s(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.

关 键 词：非齐次Dirac-调和方程 微分形式 范数不等式 权 L^s(μ)-平均域 

分 类 号：O186.15[理学—数学] O175.29[理学—基础数学]