Convex semigroups on Banach lattices

Arbeitspapier

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).

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 622

Classification and Topics

• Classification: Wirtschaft
• Subject: Convex semigroup ; nonlinear Cauchy problem ; fully nonlinear PDE ; well-posedness and uniqueness ; Hamilton-Jacobi-Bellman equations

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Denk, Robert ; Kupper, Michael ; Nendel, Max
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2019

Further information

• Handle: http://hdl.handle.net/10419/227818
• URN: urn:nbn:de:0070-pub-29372580
• Last update: 10.03.2025, 11:44 AM CET