微分形式椭圆方程障碍问题很弱解的正则性  

Regularity for Very Weak Solutions to Obstacle Problems of Elliptic Equations in differential form

作　　者：杨超 谢素英[1] YANG Chao;XIE Suying(School of Science,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2019年第3期92-96,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：浙江省自然科学基金项目(LQ17A010007)

摘　　要：研究了微分形式的非齐次椭圆方程■的κ■(Ω,Λ^(l-1))-障碍问题的很弱解。利用Hodge分解的方法及逆H?lder不等式,证明了微分形式的非齐次椭圆方程很弱解的局部正则性。由于方程包含右端项■,在证明过程中,采用对同一积分项两次使用H?lder不等式和Young不等式的技巧,得到最后的估计。This paper discusses the very weak solutions of Kφ,θ^r(Ω,A^l-1)-obstacle problems to nonhomogeneous elliptic equations in differential form d*A(x,ω(x))+B(x,ω(x),dω(x)).The local regularity of very weak solutions of obstacle problems to the nonhomogeneous elliptic equations is proved by combining the method of Hodge decomposition with reverse Holder’s inequality.Note the term B(x,ω(x),dω(x))at right side of the equation,we apply Holder’s and Young’s inequalities twice for the same integrand in the proof,which leads to the required estimates.

关 键 词：障碍问题 很弱解 HODGE分解 局部正则性 

分 类 号：O175.23[理学—数学]