Construction of bipotentials and a minimax theorem of Fan
Abstract
In Mechanics, the theory of standard materials is a well-known application of Convex Analysis. However, the so-called non-associated constitutive laws cannot be cast in the mould of the standard materials. From the mathematical viewpoint, a non associated constitutive law is a multivalued operator which is not supposed to be monotone. A possible way to study non-associated constitutive laws by using Convex Analysis, proposed first in [12], consists in constructing a "bipotential" function of two variables, which physically represents the dissipation. This is a second paper on the mathematics of the bipotentials, following math.FA/0608424 . We prove here another reconstruction theorem for a bipotential from a convex lagrangian cover, this time using a convexity notion related to a minimax theorem of Fan.
Keywords
Cite
@article{arxiv.math/0610136,
title = {Construction of bipotentials and a minimax theorem of Fan},
author = {Marius Buliga and Gery de Saxce and Claude Vallee},
journal= {arXiv preprint arXiv:math/0610136},
year = {2007}
}