An operator theoretic approach to uniform (anti-)maximum principles

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Pages (from-to)164–197
Number of pages34
JournalJournal of Differential Equations
Issue number310
Publication statusPublished - 15 Feb 2022

External IDs

researchoutputwizard legacy.publication#88127
Scopus 85121249599
unpaywall 10.1016/j.jde.2021.11.037
Mendeley f02b6b19-b0dc-3976-b55a-ba5c2b89d3e5
WOS 000754812400005


ASJC Scopus subject areas


  • Antimaximum principle, Eventual positivity, Eventually positive resolvents, Maximum principle, Uniform anti-maximum principle

Library keywords