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Journal of Convex Analysis 17 (2010), No. 1, 081--094
Copyright Heldermann Verlag 2010

Non Maximal Cyclically Monotone Graphs and Construction of a Bipotential for the Coulomb's Dry Friction Law

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

Géry de Saxcé
Laboratoire de Mécanique, Université des Sciences et Technologies, Bâtiment Boussinesq - Cité Scientifique, 59655 Villeneuve d'Ascq - Lille, France

Claude Vallée
Laboratoire de Mécanique des Solides, Bd M. et P. Curie, Téléport 2 - BP 30179, 86962 Futuroscope-Chasseneuil, France

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.

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