Curvature estimates for convex solutions of some fully nonlinear Hessian- type equations
Curvature estimates for convex solutions of some fully nonlinear Hessian- type equations
复制标题
一些完全非线性Hessian型方程凸解的曲率估计
DOI：
10.1007/s00526-019-1623-z
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Zhizhang Wang
中科院分区：
文献类型：
--
作者：
Chunhe Li;Changyu Ren;Zhizhang Wang
在完全非线性椭圆型偏微分方程的研究中，非线性算子的凹性是必不可少的。曲率估计是建立这些方程的曲率估计的关键。然而，很少有凹算子是已知的。本文给出了一些新的例子，它们是和Hessian算子和k个Hessian算子的线性组合。我们得到了这些新算子的凹性和商凹性。作为我们的凹性的应用，我们建立了由这些新算子定义的具有一般右端的方程的凸解的曲率估计。
In the research of fully nonlinear elliptic partial differential equations, the concavities of the nonlinear operators is always essential. The concavity is the key to establish the curvature estimates of these equations. However, very few concave operators are known. In the present paper, some new examples are provided, which are the sum Hessian operators and the linear combination ofkHessian operators. We obtain the concavities and the quotient concavities of these new operators. As an application of our concavities, we establish the curvature estimates of convex solutions for the equations with general right-hand side defined by these new operators.