Linear convergence in the approximation  of rank-one convex envelopes

Sören Bartels

Displaying similar documents to “Linear convergence in the approximation of rank-one convex envelopes”

A differential inclusion: the case of an isotropic set

Gisella Croce (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this article we are interested in the following problem: to find a map $u : Ω \to ℝ^{2}$ that satisfies $\{\begin{matrix} D u \in E & a.e. in Ω \\ u (x) = ϕ (x) & x \in \partial Ω \end{matrix}$ where is an open set of $ℝ^{2}$ and is a compact isotropic set of $ℝ^{2 \times 2}$ . We will show an existence theorem under suitable hypotheses on .

The steepest descent dynamical system with control. Applications to constrained minimization

Alexandre Cabot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a real Hilbert space, $Φ_{1} : H \to$ a convex function of class $𝒞^{1}$ that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system ( Brézis [CITE]) applied to the non-smooth function $Φ_{1} + δ_{S}$ . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function $Φ_{0} : H \to$ whose critical points coincide with and...

Geometric constraints on the domain for a class of minimum problems

Graziano Crasta, Annalisa Malusa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider minimization problems of the form $\min_{u \in ϕ + W_{0}^{1, 1} (Ω)} \int_{Ω} [f (D u (x)) - u (x)] d x$ where $Ω \subseteq ℝ^{N}$ is a bounded convex open set, and the Borel function $f : ℝ^{N} \to [0, + \infty]$ is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of and the zero level set of , we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.

On a Volume Constrained Variational Problem in SBV²(Ω): Part I

Ana Cristina Barroso, José Matias (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of minimizing the energy $E (u) : = \int_{Ω} {| \nabla u (x) |}^{2} d x + \int_{S_{u} \cap Ω} (1 + | [u] (x) |) d H^{N - 1} (x)$ among all functions ∈ ²(Ω) for which two level sets ${u = l_{i}}$ have prescribed Lebesgue measure $α_{i}$ . Subject to this volume constraint the existence of minimizers for (.) is proved and the asymptotic behaviour of the solutions is investigated.