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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ-limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo in un dominio limitato dello spazio -dimensionale; e sono matrici con coefficenti limitati, e è invertibile e la sua matrice inversa ha anche coefficenti limitati. La non linearità è dovuta alla funzione ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul -Laplaciano, , ed assicurano l'esistenza di una soluzione...
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 hypotheses...
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 hypotheses...
Homogenization of integral functionals is studied
under the constraint that admissible maps have to take their values
into a given smooth manifold. The notion of tangential
homogenization is defined by analogy with the tangential
quasiconvexity introduced by Dacorogna et al. [Calc. Var. Part. Diff. Eq. 9 (1999) 185–206]. For energies with superlinear or linear growth, a
Γ-convergence result is established in Sobolev spaces, the
homogenization problem in the space of functions of bounded
variation...
The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form:
, (1)
where is a set of admissible controls and is the solution of the following equation:
;
. (2).
The results are nonlocal and new.
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