and of the corresponding extension (1.3) to BV (Ω), with the aim of understanding which are the minimal assumptions on f that guarantee lower semicontinuity. Here, the starting point is the result, proved in [20], stating that if the integrand f(x, u, ξ) is a nonnegative, continuous function from Ω× IR× IR , convex in ξ, and such that the (classical) derivatives ∇xf,∇ξf,∇x∇ξf exist and are cont...

In this article, we establish sufficient conditions for the solution sets of parametric generalized quasi-variational relation problems with the stability properties such as the upper semicontinuity, lower semi-continuity, the Hausdorff lower semicontinuity, continuity, Hausdorff continuity, and closedness. Our results improve recent existing ones in the literature. Mathematics Subject Classifi...

A lower semicontinuity result is proved in the space of special functions of bounded deformation for a fracture energetic model ∫ Ju Ψ([u], νu)dH , [u] · νu ≥ 0 H − a. e. on Ju. A characterization of the energy density Ψ, which ensures lower semicontinuity, is also given.