Lipschitz Continuity

A function \(f\colon U\to \mathbb{R}\) with \(U\subset \mathbb{R}^n\) is called Lipschitz continuous, if there is a \(C>0\), such that for all \(x,y\in U\), we have

\begin{equation*} \lvert f(x)-f(y)\rvert\le C\lvert x-y\rvert. \end{equation*}