We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Γ-convergence. In contrast to what one naturally would expect, our result shows that the limiting functional is not simply a quadratic functional of the second fundamental form of the deformed plate as it is the case in nonlinear plate theory. It turns out that t...

We develop a global-in-time variational approach to the time-discretization of rate-independent processes. In particular, we investigate a discrete version of the variational principle based on the weighted energy-dissipation functional introduced in [MO08]. We prove the conditional convergence of time-discrete approximate minimizers to energetic solutions of the time-continuous problem. Moreov...

We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happ...

We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter ε, and investigate the behaviors of the minimizers when the field strength is of order O(ε−1). In this regime, we show via Γ-convergence that a chevron structure w...

The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the Γ-convergence to the initial one. AMS 2000 subject Classification: 49J45 49Q20

This talk is about two-component Bose-Einstein condensate in a harmonic trap. The aim is to describe the shape and the spatial configuration of the ground state pairs. We will show links between our model and other mathematical problems : optimal partition problems and the Cahn-Hilliard model for phase transition. These links appear in our model in the limit when intercomponent particle interac...

The quasistatic rate-independent evolution of the Prager-Zieglertype model of linearized plasticity with hardening is shown to converge to the rate-independent evolution of the Prandtl-Reuss elastic/perfectly plastic model. Based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coe cients converging to 0 by using the abstract method of Γ...

In this paper we consider the XY (N -dimensional possibly anisotropic) spin type model and, by comparison with a Ginzburg-Landau type functional, we perform a variational analysis in the limit when the number of particles diverges. In particular we show how the appearance of vortex-like singularities can be described by properly scaling the energy of the system through a Γ-convergence procedure...

In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time T if and only if its energy is negative at some time before T . The proof of this resul...

New fractional r -order seminorms, TGV r , r ∈ R , r ≥ 1 , are proposed in the one-dimensional (1D) setting, as a generalization of the integer order TGV k seminorms, k ∈ N . The fractional r -order TGV r -seminorms are shown to be intermediate between the integer order TGV k -seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect...