BLURRED MAXIMAL CYCLICALLY MONOTONE SETS AND BIPOTENTIALS

Blurred maximal cyclically monotone graphs and bipotentials

Let X be a reflexive Banach space and Y its dual. In this paper we find necessary and sufficient conditions for the existence of a bipotential for a blurred maximal cyclically monotone graph. Equivalently, we find a necessary and sufficient condition on φ ∈ Γ0(X) for that the differential inclusion y ∈ B̄(ε) + ∂φ(x) can be put in the form y ∈ ∂b(·, y)(x), with b a bipotential.

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

We show a surprising connexion between a property of the inf convolutions of a family of convex lower semicontinuous functions and the fact that intersections of maximal cyclically monotone graphs are the critical set of a bipotential. We then extend the results from [4] to bipotentials convex covers, generalizing the notion of a bi-implicitly convex lagrangian cover. As an application we prove...

Records, the Maximal Layer, and Uniform Distributions in Monotone Sets

Abatract-Consider a nondecreasing nonnegative integrable function f on [0,1]. Draw an independent sample (X1,Y1) ..... (Xn,Yn) of size n from the uniform distribution under f, and let Nn be the number of records in the sample, where (Xi,Yi) is a record when, for all j # i, either Xj > Xi or l~ < Yi. We study the dependence upon f of the constant C in the asymptotic formula ENn " CV/'ff, and sho...

Bipotentials for non monotone multivalued operators: fundamental results and applications

This is a survey of recent results about bipotentials representing multivalued operators. The notion of bipotential is based on an extension of Fenchel’s inequality, with several interesting applications related to non associated constitutive laws in non smooth mechanics, such as Coulomb frictional contact or non-associated Drücker-Prager model in plasticity. Relations betweeen bipotentials and...

Perturbations of Nonlinear Maximal Monotone Sets in Banach Space *