Smoothness of Loewner Slits

In this paper, we show that the chordal Loewner differential equation with $C^{\beta }$ driving function generates a $C^{\beta +1\mathrm{/}2}$ slit for $1/2 < \beta \leq 2$,exceptwhen$\beta = 3/2$theslitisonlyprovedtobeweakly$C^{1,1}$.