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Given a bounded open subset Ω of R d and two positive weight functions f and g, the Cheeger sets of Ω are the subdomains C of finite perimeter of Ω that maximize the ratio C f (x) dx ∂ * C g(x) dH d−1. Existence of Cheeger sets is a well-known fact. Uniqueness is a more delicate issue and is not true in general (although it holds when Ω is convex and f ≡ g(More)
La modélisation des glissements de terrain, ainsi que leprobì eme de flot maximal conduisentà considérer les ensembles de Cheeger maximaux. Dans cet article, nous donnons la forme de l'ensemble de Cheeger maximal pour différents domaines de R d. Pour cela, on montre que l'ensemble de Cheeger maximal est solution d'unprobì eme de projection assez simple que(More)
We are looking for the domains Ω ⊂ R 2 tiling the plane and functions u : Ω → R satisfying the simple impact assumption introduced by G. Buttazzo, V. Ferone and B. Kawohl [1] about the Newton's problem of the body of minimal resistance, which minimize function-als F (u; Ω) = 1 |Ω| Ω f (|∇u|), with f decreasing. We prove that only some convex polygons are(More)
This paper proposes a numerical scheme to approximate the solution of (vectorial) limit load problems. The method makes use of a strictly convex perturbation of the problem, which corresponds to a projection of the deformation field under bounded deformation and incompressibility constraints. The discretized formulation of this perturbation converges to the(More)
In this paper, we consider a model of phosphorus uptake by plant roots, governed by a quasilinear parabolic equation. We first study the well posedness of the associated Cauchy problem. Then, we consider a shape optimization problem: how to deform the shape of the root in order to increase phosphorus uptake. Finally, we give some numerical results of the(More)
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