Flow-invariant domains of Hölder continuity for nonlinear semigroups

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 $\lambda = 0$.