一类非线性椭圆方程组弱解的处处正则性  

Everywhere Regularity for Weak Solutions of a Class of Nonlinear Elliptic Equation Systems

作　　者：陈琳珏[1] 孙淑兰[1] 

机构地区：[1]佳木斯大学理学院,黑龙江省佳木斯154002

出　　处：《佳木斯大学学报（自然科学版）》2005年第2期249-252,共4页Journal of Jiamusi University：Natural Science Edition

摘　　要：　二次增长的非线性椭圆方程弱解的正则性研究已经取得了比较完备的结果,但对于方程组弱解的正则性研究取得的成果还不多,有关文献证明了对角型椭圆方程组弱解在一定条件下是Holder连续的.本文考虎一类特殊类型的非线性椭圆方程组-DαAαk(x,u,Du)=Bk(x,u,Du),k=1,2,…,N　x∈Ω Rn,在可控制增长条件下,证明其弱解是处处H lder连续的.这一结果把有关文献的结果向前推进了一步.It has appeared many results about regularity for weak solutions of quadric increasing elliptic equations. However, there are only a few results about regularity for weak solutions of nonlinear elliptic equation systems. It has been proven in literature that weak solutions of diagonal elliptic equation systems are continuous under the certain condition. Consider a class of nonlinear elliptic equation systems of the form -D_αA~α_k(x,u,Du)=B_k(x,u,Du),where k=1,2,..., N and x∈Ω R^n, and Ω is a bounded open set in R^n. It is shown that the weak solutions of the class of nonlinear elliptic equation systems are Hlder continuous under certain conditions, which generalizes the relative results in literature.

关 键 词：椭圆方程组 弱解 正则性 

分 类 号：O175.29[理学—数学]