Einladung zum Vortrag (Zoom) von Frau Sahiba Arora (TU Dresden) am 07.07.2021 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis[07.07.2021]
Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 7. Juli 2021, um 14:30 Uhr,
Frau Sahiba Arora (TU Dresden)
einen Vortrag zum Thema
Uniform maximum and anti-maximum principles.
Abstract: Extensive literature has been devoted to study the operators for which the maximum and/or the anti-maximum principle holds. Combining an idea of Takáč (1996) with those from the recent theory of eventually positive C_0-semigroups, we look at some necessary and sufficient conditions for (anti-)maximum principles to hold in an abstract setting of Banach lattices.
More precisely, if A : dom (A) \subseteq E\to E is a closed, densely defined, and real operator on a complex Banach lattice E (or in particular, an L^p-space), then we consider the equation (\lambda-A)u =f for real numbers \lambda in the resolvent set of A. We ask whether f\geq 0 implies u\geq 0 for \lambda in a right neighbourhood of an eigenvalue. In this case, we say that the maximum principle is satisfied. Analogously, when the implication f\geq 0 implies u\leq 0 holds for \lambda in a left neighbourhood of an eigenvalue, we say that the anti-maximum principle holds.
We will also see how these abstract results can be applied to various concrete differential operators and illustrate how several previously known results about (anti-)maximum principles can be proved via this theory. This is joint work with Jochen Glück.
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