一类半线性椭圆方程的解的凹性估计  

Concavity Estimations for a Class of Some Semilinear Elliptic Equations

作　　者：李丽花[1] 

机构地区：[1]上海电力学院数理系,上海200090

出　　处：《河南大学学报（自然科学版）》2009年第6期571-574,共4页Journal of Henan University:Natural Science

基　　金：上海高校选拔培养优秀青年教师科研专项基金(Z-2006-89)

摘　　要：考虑n维有界凸域Ω中的半线性椭圆方程Δu+f(u)=0,如果f(u)满足一定的条件,利用构造粘性包络的方法,证明了arcsin(u-1)及u1/2为Ω中凹函数.前者刚好满足kawohl用凹极大值原理所得出的椭圆方程的解的凸性和它的非线性项之间的关系,后者则能说明u(x)的水平集凸.Semilinear elliptic equation △u＋ f（u） = 0 in a bounded convex domain Ω in R^n, if f（u） satisfies some certain conditions, proves that arcsin（u-1） and u^1/2 are concave in Ω by using the viscosity envelope. The former result satisfies the common relationship between the convexity of solutions of some elliptic equations and its nonlinear term, which is deduced by Kawohl . The latter can reveal that the level sets of u（x） are convex .

关 键 词：粘性包络 粘性解 凹性 

分 类 号：O175.25[理学—数学]