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Construction of bipotentials and a minimax theorem of Fan

Marius Buliga·Gery de Saxce·Claude Vallee
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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.

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Marius Buliga, Gery de Saxce, Claude Vallee. 2007-02-23. Construction of bipotentials and a minimax theorem of Fan. https://arxiv.org/abs/math/0610136

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