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
e.ghahraei@sci.ui.ac.ir
Seyedehsomayeh Hosseini
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
seyedehsomayeh.hosseini@math.ethz.ch
Mohamad Reza Pouryayevali
Dept. of Mathematics, University of Isfahan, Isfahan, Iran
pourya@math.ui.ac.ir
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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