Displaying similar documents to “A variational problem for couples of functions and multifunctions with interaction between leaves”

Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

Eric Bonnetier, Richard S. Falk, Michael A. Grinfeld (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a...

General method of regularization. I: Functionals defined on BD space

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

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The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis...

General method of regularization. II: Relaxation proposed by suquet

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

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The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.

Regularization of noncoercive constraints in Hencky plasticity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

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The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

General method of regularization. III: The unilateral contact problem

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

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The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet....

A General Linear Theory of Elastic Plates and its Variational Validation

Danilo Percivale, Paolo Podio-Guidugli (2009)

Bollettino dell'Unione Matematica Italiana

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We provide a variational justification for shearable-plate models that generalize the classic Reissner-Mindlin model. Firstly, we give an argument leading to choose a fairly general linearly elastic monoclinic material response. Secondly, we prove that, for materials in such constitutive class, the variational limit of certain suitably scaled 3D energies is a functional whose minimum over a maximal subspace of admissible functions coincides with the minimum of the generalized Reissner-Mindlin...

Line-energy Ginzburg-Landau models : zero-energy states

Pierre-Emmanuel Jabin, Felix Otto, BenoÎt Perthame (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and...