Displaying similar documents to “Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth”

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

Zhiping Li (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

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

Similarity:

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...

Quasiconvex relaxation of multidimensional control problems with integrands (, , )

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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 The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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...

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

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

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

-convergence and absolute minimizers for supremal functionals

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

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

Weak notions of jacobian determinant and relaxation

Guido De Philippis (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.

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...

Weak notions of Jacobian determinant and relaxation

Guido De Philippis (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.