arXiv subjects

Margarida Baia

Publications and source records attributed to Margarida Baia.

4 recordsLinked to original sources

arXiv2016

Generalized $\mathbf{W^{1,1}}$-Young measures and relaxation of problems with linear growth

We completely characterize generalized Young measures generated by sequences of gradients of maps from $W^{1,1}(Ω;\R^M)$ where $Ω\subset\R^N$. This extends and completes previous analysis by Kristensen and Rindler where concentrations of the sequence of gradients at the boundary of $Ω$ were excluded. We apply our results to relaxation of non-quasiconvex variational problems with linear growth at infinity. We also link our characterization to Souček spaces \cite{soucek}, an extension of $W^{1,1}(Ω;\R^M)$ where gradients are considered as measures on $\barΩ$.

math.AP↗

arXiv2007

Characterization of two-scale gradient Young measures and application to homogenization

This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.

math.AP↗

arXiv2006

3D-2D analysis of a thin film with periodic microstructure

The purpose of this article is to study the behavior of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a 3D-2D dimensional reduction through a $Γ$-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.

math.AP↗

arXiv2006

Multiscale nonconvex relaxation and application to thin films

$Γ$-convergence techniques are used to give a characterization of the behavior of a family of heterogeneous multiple scale integral functionals. Periodicity, standard growth conditions and nonconvexity are assumed whereas a stronger uniform continuity with respect to the macroscopic variable, normally required in the existing literature, is avoided. An application to dimension reduction problems in reiterated homogenization of thin films is presented.

math.AP↗