一类半线性椭圆边值问题解的梯度估计  

Gradient Estimates of Solutions for a Class of Semilinear Elliptic Boundary Value Problems

作　　者：兰乃端[1] 常保平[2] 

机构地区：[1]山西财贸职业技术学院,山西太原030031 [2]安阳师范学院,河南安阳455002

出　　处：《山西大学学报（自然科学版）》2005年第3期241-243,共3页Journal of Shanxi University(Natural Science Edition)

摘　　要：运用Hopf极值原理讨论了一类具有Dirichlet边界条件u=0的半线性椭圆方程Δu+f(x,u,q)=0(q=|u|2)的解的某个函数的极值原理,利用该结论获得了解的梯度q的估计.The maximum principles for functions which are defined on solutions of semilinear elliptic equations △u＋f（x，u，q）=0（q=｜↓△u｜^2）subject to Dirichlet boundary conditions u = 0 were studied by using Hopf＇s maximum principle,the estimate of gradient q was obtained.

关 键 词：半线性椭圆方程 极值原理 梯度估计 

分 类 号：O175.2[理学—数学]