A characterization of the individual maximum and anti-maximum principle

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Article number24
Number of pages17
JournalMathematische Zeitschrift
Issue number2
Publication statusPublished - Oct 2023

External IDs

Scopus 85172005763
Mendeley 09bfe9da-2f5a-3bac-aad4-2dc227b2e0e3


DFG Classification of Subject Areas according to Review Boards

ASJC Scopus subject areas


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

Library keywords