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

Zsolt Páles; Vera Zeidan

doi:10.3934/dcds.2011.29.623

Article Contents

2011, Volume 29, Issue 2: 623-646. Doi: 10.3934/dcds.2011.29.623

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

Zsolt Páles^1, and
Vera Zeidan^2,

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

Received: August 31, 2009

Revised: February 28, 2010

Published: May 2011

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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.

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Mathematics Subject Classification: 49J52, 49A52, 58C20.

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