Displaying similar documents to “Variational approximation for detecting point-like target problems”

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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

Dimension reduction for −Δ1

Maria Emilia Amendola, Giuliano Gargiulo, Elvira Zappale (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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A 3D-2D dimension reduction for −Δ is obtained. A power law approximation from −Δ as  → 1 in terms of -convergence, duality and asymptotics for least gradient functions has also been provided.

-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...

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....

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.

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in -norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate information of smoothness/sparsity on the inhomogeneity...

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization

Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large- result of [M. Griesemer and F. Hantsch, (2011) 170]. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large- result of [M. Griesemer and F. Hantsch, (2011) 170]. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient...

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.

Linearized plastic plate models as Γ-limits of 3D finite elastoplasticity

Elisa Davoli (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of -convergence, in the framework of finite plasticity. Denoting by the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order , with ≥ 3. According to the value of , partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory...

Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands

Micol Amar, Virginia De Cicco, Nicola Fusco (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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New -lower semicontinuity and relaxation results for integral functionals defined in BV() are proved, under a very weak dependence of the integrand with respect to the spatial variable . More precisely, only the lower semicontinuity in the sense of the -capacity is assumed in order to obtain the lower semicontinuity of the functional. This condition is satisfied, for instance, by the lower approximate limit of the integrand, if it is BV with respect to . Under this further...

The H–1-norm of tubular neighbourhoods of curves

Yves van Gennip, Mark A. Peletier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the -norm of the function 1 on tubular neighbourhoods of curves in ℝ 2 . We take the limit of small thickness, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit → 0, containing contributions from the length of the curve (at order ), the ends ( ), and the curvature ( ). The second result is a Γ-convergence result, in which the central curve may vary along...