一类非线性椭圆问题解的正则性

Regularity for some nonlinear elliptic problems

研究椭圆型偏微分方程的源函数是关于自变量、自变量的未知函数及未知函数的偏导数的函数时,非线性椭圆方程的边值问题.利用推广的Stampacchia引理以及Sobolev空间的分析技巧,得到椭圆型方程的边值问题在强制性和控制增长条件下解的正则性.

When the source function of elliptic partial differential equation is a function of independent variable,unknown function of independent variable and partial derivative of unknown function,the boundary value problem of nonlinear elliptic equation is studied.By using the generalized Stampacchia lemma and the analysis technique of Sobolev space,the regularity of the solution of the boundary value problem of elliptic equation under some coercivity and controlled growth assumptions is obtained.