Displaying similar documents to “An existence result for a nonconvex variational problem via regularity”

Regularity results for an optimal design problem with a volume constraint

Menita Carozza, Irene Fonseca, Antonia Passarelli di Napoli (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with -power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (), Hölder continuity of the function is proved as well as partial regularity of the boundary of the minimal set . Moreover, full regularity of the boundary of the minimal...

The polarization in a ferroelectric thin film: local and nonlocal limit problems

Antonio Gaudiello, Kamel Hamdache (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, starting from classical non-convex and nonlocal 3-variational model of the electric polarization in a ferroelectric material, an asymptotic process we obtain a rigorous 2-variational model for a thin film. Depending on the initial boundary conditions, the limit problem can be either nonlocal or local.

-convergence and absolute minimizers for supremal functionals

Thierry Champion, Luigi De Pascale, Francesca Prinari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we prove that the approximants naturally associated to a supremal functional -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer...

Regularization of an unilateral obstacle problem

Ahmed Addou, E. Bekkaye Mermri, Jamal Zahi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this article is to give a regularization method for an unilateral obstacle problem with obstacle and second member , which generalizes the one established by the authors of [4] in case of null obstacle and a second member is equal to constant .

Variational approximation for detecting point-like target problems

Gilles Aubert, Daniele Graziani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to provide a rigorous variational formulation for the detection of points in -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 -convergence to the initial one.

Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands (, , ) in presence of a convex control restriction. The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image...