Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/324260 
Year of Publication: 
2020
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 716
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
We consider convex monotone semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a σ -Dedekind complete Banach lattice with an additional assumption on the dual space. As typical examples, we consider the space of bounded uniformly continuous functions and the space of continuous functions vanishing at infinity. We show that the domain of the classical generator for convex monotone C0-semigroups, which is defined in terms of the time derivative at 0 w.r.t. the supremum norm, is typically not invariant. We thus propose alternative forms of generators and domains, for which we prove the invariance under the semigroup. As a consequence, we obtain the uniqueness of the semigroup in terms of an extended version of the generator. The results are discussed in several examples related to fully nonlinear partial differential equations, such as uncertain shift semigroups and semigroups related to G-heat equations (fully nonlinear versions of the heat equation).
Subjects: 
Convex semigroup
nonlinear Cauchy problem
fully nonlinear PDE
uniqueness
Hamilton-Jacobi-Bellman equation
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

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