An operator theoretic approach to uniform (anti-)maximum principles
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
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.
Details
Original language | English |
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Pages (from-to) | 164–197 |
Number of pages | 34 |
Journal | Journal of Differential Equations |
Volume | 310 |
Issue number | 310 |
Publication status | Published - 15 Feb 2022 |
Peer-reviewed | Yes |
External IDs
researchoutputwizard | legacy.publication#88127 |
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Scopus | 85121249599 |
unpaywall | 10.1016/j.jde.2021.11.037 |
Mendeley | f02b6b19-b0dc-3976-b55a-ba5c2b89d3e5 |
WOS | 000754812400005 |
Keywords
ASJC Scopus subject areas
Keywords
- Antimaximum principle, Eventual positivity, Eventually positive resolvents, Maximum principle, Uniform anti-maximum principle