摘要
本文给出了方程△u+■b_i(x)D_iu=f(u)解的梯度界,并导出相应的Liouville定理。
In this paper we prove the following theorem.Let F∈C^2(R)be a non-negative function and u∈C^3(R^n)a solution in all ofR^n of the equationwhere f=F is the first derivative of F,is bounded on R^n and(D_jb_i(x)_(n×n) negativesemidefinite matrices.If u is bounded on R^n,then |Du|~2(x)≤2F(u(x))for everyx∈R^n.Also we obtain an Liouville theorem:If there exists x_0∈R^nsuch that F(u(x_0))=0,and the assumptions of the above theorem holds,then u is constant.
出处
《晓庄学院自然科学学报》
CAS
1990年第3期200-203,共4页
Journal of Natural Science of Hunan Normal University
