The sharp Whitney extension theorem for convex $C^1$ Lipschitz functions

Carlos Mudarra

For an arbitrary set $E\subset {\mathbb{R}}^n$, and functions $f:E\to \mathbb{R}$, $G:E\to {\mathbb{R}}^n$ with $G$ bounded, we construct $C^1({\mathbb{R}}^n)$ convex extensions $(F,…