Hölder Condition

A function $\phi(t)$ satisfies the Hölder condition on two points $t_1$ and $t_2$ on an arc $L$ when

$$\vert\phi(t_2)-\phi(t_1)\vert\leq A\vert t_2-t_1\vert^\mu,$$

with $A$ and $\mu$ Positive Real constants.