The uniqueness as a generic property for some one-dimensional segmentation problems
Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands
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 BV dependence, a...
Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands
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 BV dependence, a...
A relaxation result in BV for integral functionals with discontinuous integrands
We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.
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