Displaying similar documents to “Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set”

An existence result for a nonconvex variational problem via regularity

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the...

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

Nicola Fusco, Virginia De Cicco, Micol Amar (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

New L 1 -lower semicontinuity and relaxation results for integral functionals defined in BV( Ω ) are proved, under a very weak dependence of the integrand with respect to the spatial variable x . More precisely, only the lower semicontinuity in the sense of the 1 -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 x . Under this further BV dependence,...