Myriam Comte

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Given a bounded open subset Ω of Rd 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 ≡(More)
We are looking for the domains Ω ⊂ R 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 functionals 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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