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Flow-invariant domains of Hölder continuity for nonlinear semigroups

Author: Andrew T. Plant
Journal: Proc. Amer. Math. Soc. 53 (1975), 83-87
MSC: Primary 47H05
MathSciNet review: 0377611
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Abstract: Let $ S(t)$ be a nonlinear semigroup, on Banach space $ X$, generated by an accretive set $ A$. The set of $ x$ in $ X$ such that $ t \to S(t)x$ is Hölder continuous, with Hölder exponent $ \sigma \,\epsilon \,(0,\;1]$, is flow-invariant and is characterised by the behaviour of the map $ \lambda \to {(I + \lambda A)^{ - 1}}x$ at $ \lambda = 0$.

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Keywords: Banach space, nonlinear semigroup, accretive set, flow-invariant, Hölder continuous
Article copyright: © Copyright 1975 American Mathematical Society

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