On driving functions generating quasislits in the chordal   Loewner-Kufarev equation
  We prove that for every $C>0$ there exists a driving function $U:[0,1]\to\mathbb{R}$ such that the corresponding chordal Loewner-Kufarev equation generates a quasislit and $ \limsup_{h\downarrow0}\frac{|U(1)-U(1-h)|}{\sqrt{h}}=C. $ 
Sebastian Schleissinger
math.CV