Functions with constant generalized gradients (Q1813907)

The following result is established: Theorem 1. Let \(K\) be a nonempty convex compact subset of \(\mathbb{R}^ n\). Then there exists a Lipschitz function \(F: \mathbb{R}^ n\to \mathbb{R}\) such that, for all \(x\in\mathbb{R}^ n\), \(K=\partial F_ K(x)\), where \(\partial\) stands for Clarke's generalized gradient.