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Journal of Convex Analysis 24 (2017), No. 1, 149--168
Copyright Heldermann Verlag 2017

Pseudo-Jacobian and Characterization of Monotone Vector Fields on Riemannian Manifolds

E. Ghahraei
Dept. of Mathematics, University of Isfahan, Isfahan, Iran

Seyedehsomayeh Hosseini
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

Mohamad Reza Pouryayevali
Dept. of Mathematics, University of Isfahan, Isfahan, Iran

A notion of pseudo-Jacobian of continuous vector fields on Riemannian manifolds is presented. It is shown that the Clarke generalized Jacobian and Mordukhovich coderivative for locally Lipschitz vector fields are pseudo-Jacobians. Moreover, monotone vector fields are characterized in terms of pseudo-Jacobians.

Keywords: Pseudo-Jacobian, Lipschitz vector fields, Monotone vector fields, Riemannian manifolds.

MSC: 58C20, 49J52, 47H05

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