A characterization of the individual maximum and anti-maximum principle

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

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.

Details

OriginalspracheEnglisch
Aufsatznummer24
Seitenumfang17
FachzeitschriftMathematische Zeitschrift
Jahrgang305
Ausgabenummer2
PublikationsstatusVeröffentlicht - Okt. 2023
Peer-Review-StatusJa

Externe IDs

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

Schlagworte

DFG-Fachsystematik nach Fachkollegium

ASJC Scopus Sachgebiete

Schlagwörter

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