论文标题
个体最大和反量最大原理的特征
A characterization of the individual maximum and anti-maximum principle
论文作者
论文摘要
差分运算符的最大和反量最大原理的抽象方法通常依赖于操作员域中的所有向量都以操作员的领先特征功能为主导的条件。我们研究这种情况的必要性。特别是，我们表明，在许多自然假设下，当且仅当满足上述统治条件时，同时保持最大和反量最大原理的所谓单个版本。 因此，我们能够证明各种具体的差异算子不满足反量最大原则。
Abstract approaches to maximum and anti-maximum principles for differential operators typically rely on the condition that all vectors in the domain of the operator are dominated by the leading eigenfunction of the operator. We study the necessity of this condition. In particular, we show that under a number of natural assumptions, so-called individual versions of both the maximum and the anti-maximum principle simultaneously hold if and only if the aforementioned domination condition is satisfied. Consequently, we are able to show that a variety of concrete differential operators do not satisfy an anti-maximum principle.
