Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law

Details Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law

2008-02-08

arxiv.org/abs/0802.1140v4

J. of Convex Analysis 17, No 1. (2010)

Mathematics

Functional Analysis

accepted by the Journal of Convex Analysis

Scientific paper

We show a surprising connexion between a property of the inf convolution of a family of convex lower semicontinuous functions and the fact that the intersection of maximal cyclically monotone graphs is the critical set of a bipotential. We then extend the results from arXiv:math/0608424v4 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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