Convex Semigroups on Banach Lattices
Robert Denk (),
Michael Kupper and
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Michael Kupper: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University
No 622, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University
In this paper, we investigate convex semigroups on Banach lattices. First, we consider the case, where the Banach lattice is $\sigma$-Dedekind complete and satisfies a monotone convergence property, having L$^p$--spaces in mind as a typical application. Second, we consider monotone convex semigroups on a Banach lattice, which is a Riesz subspace of a $\sigma$-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).
Keywords: Convex semigroup; nonlinear Cauchy problem; fully nonlinear PDE; well-posedness and uniqueness; Hamilton-Jacobi-Bellman equations (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:622
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