On the Construction of Hölder and Proximal Subderivatives
On the Construction of Hölder and Proximal Subderivatives
Abstract We construct Lipschitz functions such that for all s > 0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.