$V$-Jacobian and $V$-co-Jacobian for Lipschitzian maps

Abstract

The notions of $V$-Jacobian and $V$-co-Jacobian are introduced for locally Lipschitzian functions acting between arbitrary normed spaces $X$ and $Y$, where $V$ is a subspace of the dual space $Y^*$. The main results of this paper provide a characterization, calculus rules and also the computation of these Jacobians of piecewise smooth functions.