一致（反）最大值原理的算子理论方法
An operator theoretic approach to uniform (anti-)maximum principles
AI总结：
本文融合Takáč的抽象算子理论思想与最终正算子半群新进展，给出一般情形下（反）最大值原理的充要条件，并用于判定和解释多种微分算子的相关性质。
摘要：
最大值原理与一致反最大值原理是PDE理论中一个普遍存在的课题，与Krein–Rutman定理以及预解式的核估计密切相关。我们采纳Takáč的一个经典思想——在抽象算子理论框架中证明（反）最大值原理——并将其与最终正算子半群理论的近期思想相结合。这使我们能够在非常一般的设定下导出（反）最大值原理的充要条件。因此，对于大量具体的微分算子，我们既能够证明也能够证伪（反）最大值原理。此外，对于若干已知满足或不满足反最大值原理的算子，我们的理论为这种行为提供了非常清晰简洁的解释。
英文摘要：
Maximum principles and uniform anti-maximum principles are a ubiquitous topic in PDE theory that is closely tied to the Krein--Rutman theorem and kernel estimates for resolvents. We take up a classical idea of Takáč - to prove (anti-)maximum principles in an abstract operator theoretic framework - and combine it with recent ideas from the theory of eventually positive operator semigroups. This enables us to derive necessary and sufficient conditions for (anti-)maximum principles in a very general setting. Consequently, we are able to either prove or disprove (anti-)maximum principles for a large variety of concrete differential operators. As a bonus, for several operators that are already known to satisfy or to not satisfy anti-maximum principles, our theory gives a very clear and concise explanation of this behaviour.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
