On New Structures in the Theory of Fully Nonlinear Equations
On New Structures in the Theory of Fully Nonlinear Equations
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论完全非线性方程理论中的新结构
DOI：
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发表时间：
2018
影响因子：
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通讯作者：
N. Filimonenkova
中科院分区：
文献类型：
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作者：
N. Ivochkina;N. Filimonenkova
我们用 m-Hessian 平稳算子和演化算子描述了方程论的当前状态。这个理论中出现新的代数和几何概念是相当重要的。在当前的工作中，提供了这些概念的列表。其中，矩阵的m正性概念相当重要；我们提供了此类矩阵的西尔维斯特准则的类似证明。根据这个准则，我们很容易得到m-Hessian演化方程第一初始边值问题经典解存在的充要条件。半有界圆柱体中 m-Hessian 演化的渐近行为也被考虑。
We describe the current state of the theory of equations with m-Hessian stationary and evolution operators. It is quite important that new algebraic and geometric notions appear in this theory. In the present work, a list of those notions is provided. Among them, the notion of m-positivity of matrices is quite important; we provide a proof of an analog of Sylvester’s criterion for such matrices. From this criterion, we easily obtain necessary and sufficient conditions for existence of classical solutions of the first initial boundary-value problem for m-Hessian evolution equations. The asymptotic behavior of m-Hessian evolutions in a semibounded cylinder is considered as well.