Bipotentials for Non-monotone Multivalued Operators: Fundamental Results and Applications
نویسندگان
چکیده
منابع مشابه
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...
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In this paper, some properties of pre-monotone operators are proved. It is shown that in a reflexive Banach space, a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous. The notion of $sigma$-convexity is introduced and the relations between the $sigma$-monotonicity and $sigma$-convexity is i...
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Based on an extension of Fenchel inequality, bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Let X , Y be dual locally convex spaces, with duality product 〈·, ·〉 : X×Y → R. Given the graph M ⊂ X × Y of a multivalued law T : X → 2 , we state a ...
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Bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Given by a graph M representing a multivalued constitutive law, we state a simple necessary and sufficient condition for the existence of a bipotential b for which M is the set of (x, y) such tha...
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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.
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ژورنال
عنوان ژورنال: Acta Applicandae Mathematicae
سال: 2009
ISSN: 0167-8019,1572-9036
DOI: 10.1007/s10440-009-9488-3