Abstract

We show a surprising connection between a property of the inf convolution of a family of convex lsc functions and the fact that the intersection of maximal cyclically monotone graphs is the critical set of a bipotential. We then extend our previous results published in this journal [J. Convex Analysis 15(1) (2008) 87–104] to bipotentials convex covers, generalizing the notion of a bi-implicitly convex lagrangian cover. As an application we prove that the bipotential related to Coulomb's friction law is related to a specific bipotential convex cover with the property that any graph of the cover is non maximal cyclically monotone

Author information

Contact details are reproduced from the original publication and may be historical.

Marius Buliga

"Simion Stoilow" Inst. of Mathematics, Romanian Academy of Sciences, P. O. Box 1-764, 014700 Bucharest, Romania

Marius.Buliga@imar.ro

Géry de Saxcé

Laboratoire de Mécanique, Université des Sciences et Technologies, Bâtiment Boussinesq - Cité Scientifique, 59655 Villeneuve d'Ascq - Lille, France
and: UMR CNRS 8107

gery.desaxce@univ-lille1.fr

Claude Vallée

Laboratoire de Mécanique des Solides, Bd M. et P. Curie, Téléport 2 - BP 30179, 86962 Futuroscope-Chasseneuil, France
and: UMR CNRS 6610

vallee@lms.univ-poitiers.fr

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Suggested citation

M. Buliga, G. de Saxcé, C. Vallée. “Non Maximal Cyclically Monotone Graphs and Construction of a Bipotential for the Coulomb's Dry Friction Law.” Journal of Convex Analysis 17 (2010), No. 1, 81–94. https://doi.org/10.68381/jca17007

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.