# American Institute of Mathematical Sciences

April  2011, 29(2): 623-646. doi: 10.3934/dcds.2011.29.623

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

 1 Institute of Mathematics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary 2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States

Received  September 2009 Revised  March 2010 Published  October 2010

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.
Citation: Zsolt Páles, Vera Zeidan. $V$-Jacobian and $V$-co-Jacobian for Lipschitzian maps. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 623-646. doi: 10.3934/dcds.2011.29.623
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