Displaying similar documents to “Homogenization of variational problems in manifold valued Sobolev spaces”

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 ) = ∫ Ω φ x , x ε , m ( x ) d x - ∫ Ω h e ( x ) · m ( x ) d x + 1 2 ∫ ℝ 3 | ∇ u ( x ) | 2 d x of a large ferromagnetic body is obtained.

Equi-integrability results for 3D-2D dimension reduction problems

Marian Bocea, Irene Fonseca (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients ∇ α u ε | 1 ε ∇ 3 u ε bounded in L p ( Ω ; ℝ 9 ) , 1 < p < + ∞ . Here it is shown that, up to a subsequence, u ε may be decomposed as w ε + z ε , where z ε carries all the concentration effects, i.e. ∇ α w ε | 1 ε ∇ 3 w ε p is equi-integrable, and w ε captures the oscillatory behavior, i.e. z ε → 0 in measure. In addition, if { u ε } is a recovering sequence then z ε = z ε ( x α ) nearby ∂ Ω .

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.