一类椭圆型方程障碍问题很弱解的局部正则性  

Local Regularity for Very Weak Solutions of Obstacle Problems to a Class of Elliptic Equation

作　　者：谢素英[1] 许明雷[1] 赵娜[1] 

机构地区：[1]杭州电子科技大学理学院数学系,浙江杭州310018

出　　处：《应用数学》2012年第4期707-712,共6页Mathematica Applicata

基　　金：国家自然科学基金项目(10871126;11171307)

摘　　要：本文研究一类非齐次二阶椭圆型方程-divA(x,u,Du)=B(x,u,Du)的Krψ,θ(Ω)-障碍问题的很弱解.利用Hodge分解的方法及逆Hlder不等式,给出非齐次方程的障碍问题很弱解的局部正则性.由于B(x,u,Du)中u和Du的增长指数为次临界,为了得到局部正则性,我们对同一积分项使用了两次Young和Hlder不等式的技巧.This paper study the very weak solutions of Kφr（Ω） -obstacle problems to a class of nonhomogeneous elliptic quation of second order -- divA（x,u,Du） = B（x,u,Du）, We obtain a local regularity of very weak solutions of obstacle problems to the nonhomoge- neous elliptic equation by using the method of Hodge decomposition and reverse HOlder ine- quality. To obtain the local regularity,we apply HOlder and Young ineuqalities twice for the same lntegran Du. d since the growth exponents of B（x,u,Du） are subcrtical with respect to u and Du.

关 键 词：障碍问题 很弱解 HODGE分解 局部正则性 

分 类 号：O175.25[理学—数学]