Feller generators with measurable lower order terms

Kühn, Franziska; Kunze, Markus

doi:10.1007/s11117-022-00948-4

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(B) It Follows From Proposition1

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2023

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Cited by 2 publications

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“…Following [23], we say that a subset C ⊂ L full is an bp-core, if L full is the bp-closure of C. We next give a criterion for a bp-core.…”

Section: (B) It Follows From Propositionmentioning

confidence: 99%

Convex semigroups on $$L^p$$-like spaces

2021

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In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ L p -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ C 0 -semigroup theory extend to the convex case. We prove that the generator of a convex $$C_0$$ C 0 -semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup, a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of $$C_0$$ C 0 -semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.

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“…Following [23], we say that a subset C ⊂ L full is an bp-core, if L full is the bp-closure of C. We next give a criterion for a bp-core.…”

Section: (B) It Follows From Propositionmentioning

confidence: 99%