Yau's gradient estimates for a nonlinear elliptic equation
Yau's gradient estimates for a nonlinear elliptic equation
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非线性椭圆方程的丘氏梯度估计
DOI：
10.1007/s00013-016-0983-2
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发表时间：
2017-04-01
影响因子：
0.6
通讯作者：
Qian, Bin
中科院分区：
文献类型：
--
作者：
Qian, Bin
设（M-n，g）是n维完备黎曼流形.考虑非线性方程Delta u + Au log u = 0正解的Yau梯度估计，其中a是常数.作为应用，我们得到了该方程在a < 0时的Liouville性质.此外，我们通过具体的例子说明，我们的结果是尖锐的。
Let (M-n, g) be an n-dimensional complete Riemannian manifold. We consider Yau's gradient estimates for positive solutions to the following nonlinear equationDelta u + au log u = 0where a is a constant. As an application, we obtain the Liouville property for this equation in the case of a < 0. In addition, we illustrate, by giving concrete examples, that our results are sharp.