Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/227818 
Erscheinungsjahr: 
2019
Schriftenreihe/Nr.: 
Center for Mathematical Economics Working Papers No. 622
Verlag: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Zusammenfassung: 
In this paper, we investigate convex semigroups on Banach lattices. First, we consider the case, where the Banach lattice is σ-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 σ-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).
Schlagwörter: 
Convex semigroup
nonlinear Cauchy problem
fully nonlinear PDE
well-posedness and uniqueness
Hamilton-Jacobi-Bellman equations
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