TY  - GEN
AB  - 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).
DA  - 2019
KW  - Convex semigroup
KW  - nonlinear Cauchy problem
KW  - fully nonlinear PDE
KW  - well-posedness and uniqueness
KW  - Hamilton-Jacobi-Bellman equations
LA  - eng
PY  - 2019
SN  - 0931-6558
SP  - 36-
TI  - Convex Semigroups on Banach Lattices
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29372580
Y2  - 2024-11-22T05:14:56
ER  -