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Displaying similar documents to “Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands”

Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set

Luciano Carbone, Doina Cioranescu, Riccardo De Arcangelis, Antonio Gaudiello (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness...

Integral representation and Γ -convergence of variational integrals with p ( x ) -growth

Alessandra Coscia, Domenico Mucci (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the integral representation properties of limits of sequences of integral functionals like ∫ f ( x , D u ) d x under nonstandard growth conditions of ( p , q ) -type: namely, we assume that | z | p ( x ) ≤ f ( x , z ) ≤ L ( 1 + | z | p ( x ) ) . Under weak assumptions on the continuous function p ( x ) , we prove Γ -convergence to integral functionals of the same type. We also analyse the case of integrands f ( x , u , D u ) depending explicitly on u ; finally we weaken the assumption allowing p ( x ) to be discontinuous on nice sets.

An existence result for a nonconvex variational problem via regularity

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the...

On the unique extension problem for functionals of the calculus of variations

Luciano Carbone, Riccardo De Arcangelis (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of R n and every function in C ∞ ⁢ R n , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider...