A relaxation result for energies defined on pairs set-function and applications

Andrea Braides; Antonin Chambolle; Margherita Solci

Displaying similar documents to “A relaxation result for energies defined on pairs set-function and applications”

Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi, Enrico Vitali (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.

Relaxation of free-discontinuity energies with obstacles

Matteo Focardi, Maria Stella Gelli (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Given a Borel function defined on a bounded open set with Lipschitz boundary and $ϕ \in L^{1} (\partial Ω, ℋ^{n - 1})$ , we prove an explicit representation formula for the lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint $u^{+} \geq ψ$ $ℋ^{n - 1}$ a.e. on and the Dirichlet boundary condition $u = ϕ$ on $\partial Ω$ .

Homogenization of micromagnetics large bodies

Giovanni Pisante (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies $ℰ_{ε} (m) = \int_{Ω} φ (x, \frac{x}{ε}, m (x)) d x - \int_{Ω} h_{e} (x) \cdot m (x) d x + \frac{1}{2} \int_{ℝ^{3}} {| \nabla u (x) |}^{2} d x$ of a large ferromagnetic body is obtained.

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the $Γ$ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.