Displaying similar documents to “Γ-convergence and absolute minimizers for supremal functionals”

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...

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....

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...

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains a construction of quasiconvex functions with linear growth.

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...

Semi-continuité inférieure d'intégrales multiples et d'intégrandes convergentes

Zhiping Li (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity of multiple integrals ∫ and ∫ are studied. It is proved that the two can derive from each other under certain general hypotheses such as uniform lower compactness property and locally uniform convergence of . The result is applied to obtain some general lower semicontinuity theorems on multiple integrals with quasiconvex integrand ƒ, while are not required to be quasiconvex.

Some aspects of the local theory of generalized Dhombres functional equations in the complex domain

Jörg Tomaschek (2012)

ESAIM: Proceedings

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We study the generalized Dhombres functional equation (()) = (()) in the complex domain. The function is given and we are looking for solutions with (0) =  and is a primitive root of unity of order  ≥ 2. All formal solutions for this case are described in this work, for the situation where can be transformed into a function which is linearizable and local analytic in a neighbourhood...

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...