Convex semigroups on Banach lattices / Robert Denk, Michael Kupper and Max Nendel
VerfasserDenk, Robert In der Gemeinsamen Normdatei der DNB nachschlagen ; Kupper, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Nendel, Max
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, September 2019
Elektronische Ressource
Umfang1 Online-Ressource (35 Seiten)
SerieCenter for Mathematical Economics Working papers ; 622
SchlagwörterHamilton-Jacobi-Differentialgleichung In Wikipedia suchen nach Hamilton-Jacobi-Differentialgleichung / Cauchy-Anfangswertproblem In Wikipedia suchen nach Cauchy-Anfangswertproblem
URNurn:nbn:de:hbz:6:2-121925 Persistent Identifier (URN)
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Convex semigroups on Banach lattices [0.47 mb]

In this paper, we investigate convex semigroups on Banach lattices. First, we consider the case, where the Banach lattice is -Dedekind complete and satisfies a monotone convergence property, having Lp-spaces in mind as a typical application. Second, we consider monotone convex semigroups on a Banach lattice, which is a Riesz subspace of a -Dedekind complete Banach lattice, where we consider the space of bounded uniformly continuous functions as a typical example. In both cases, we prove the invariance of a suitable domain for the generator under the semigroup. As a consequence, we obtain the uniqueness of the semigroup in terms of the generator. The results are discussed in several examples such as semilinear heat equations (g-expectation), nonlinear integro-differential equations (uncertain compound Poisson processes), fully nonlinear partial differential equations (uncertain shift semigroup and G-expectation).