一类微分形式的椭圆方程很弱解梯度的零点  

Zeros of Very Weak Solution Gradients for a Class of Differential Form Elliptic Equations

作　　者：康迪 赵崧 徐秀娟 KANG Di;ZHAO Song;XU Xiujuan(College of Science,North China University of Technology,Tangshan Hebei 063210,China;Hebei Key Laboratory of Data Science and Application,Tangshan Hebei 063210,China)

机构地区：[1]华北理工大学理学院,河北唐山063210 [2]河北省数据科学与应用重点实验室,河北唐山063210

出　　处：《西南师范大学学报（自然科学版）》2023年第3期25-30,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：河北省自然科学基金项目(A2019209533)。

摘　　要：文章考虑了一类微分形式的椭圆方程,通过Hodge分解、 Poincaré不等式等工具,证明了其很弱解的梯度满足弱逆H9lder不等式,并得到了该方程很弱解梯度的几乎每一个零点都有无穷阶.The article considers a class of differential form elliptic equations,and proves that the gradient of their very weak solutions satisfies the weak inverse H9lder inequality by tools such as Hodge decomposition,Poincaré inequality,and obtains that almost every zero of the gradient of the very weak solutions of this equation has infinite order.

关 键 词：微分形式 很弱解 HODGE分解 零点 

分 类 号：O175.23[理学—数学]