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- Marco Barchiesi
- 2006

This article is devoted to obtain the Γ-limit, as ε tends to zero, of the family of functionals u 7→ ∫ Ω f ( x, x ε , . . . , x ε ,∇u(x) ) dx, where f = f(x, y, . . . , yn, z) is periodic in y, . . . , yn, convex in z and satisfies a very weak regularity assumption with respect to x, y, . . . , yn. We approach the problem using the multiscale Young measures.

- Marco Barchiesi
- 2006

This article is devoted to the study of the asymptotic behavior of the zero-energy deformations set of a periodic nonlinear composite material. We approach the problem using two-scale Young measures. We apply our analysis to show that polyconvex energies are not closed with respect to periodic homogenization. The counterexample is obtained through a… (More)

In this article we show that for the homogenization of multiple integrals, the quasiconvexification of the cell formula is different from the asymptotic formula in general. To this aim, we construct three examples in three different settings: the homogenization of a discrete model, the homogenization of a composite material and the homogenization of a… (More)

- Marco Barchiesi, Gianni Dal Maso
- SIAM J. Math. Analysis
- 2009

We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period ε of the grid and the ratio δ between the thickness of the fibers and the period ε. We show that the asymptotic behavior as… (More)

We define a class of deformations in W (Ω,R), p > n−1, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality Det = det (that the distributional determinant coincides with the pointwise determinant of the gradient). Maps in this class are shown to satisfy a… (More)

- Marco Barchiesi, Giuliano Lazzaroni, Caterina Ida Zeppieri
- SIAM J. Math. Analysis
- 2016

- Marco Barchiesi
- 2008

We analyze the asymptotic behavior of the antiplane deformations of a fragile material reinforced by a reticulated elastic structure. The microscopic geometry of this material is described by means of two “small” parameters: the size ε of the periodic grid and the ratio δ between the thickness of each of the fibers and their period of distribution. We show… (More)

- Marco Barchiesi
- 2011

The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.

- Marco Barchiesi
- 2005

This article is devoted to obtain the Γ-limit, as ε tends to zero, of the family of functionals u 7→ ∫ Ω f ( x, x ε , . . . , x ε ,∇u(x) ) dx, where f = f(x, y, . . . , yn, z) is periodic in y, . . . , yn, convex in z and satisfies a very weak regularity assumption with respect to x, y, . . . , yn. We approach the problem using the multiscale Young measures.

- Marco Barchiesi
- 2014

A quantitative version of Pólya-Szegő inequality is proven for log-concave functions in the case of Steiner and Schwarz rearrangements.