Lower semicontinuity viaW1,q-quasiconvexity

A - Quasiconvexity , Lower Semicontinuity And

Lower semicontinuity of surface energies

On L-lower semicontinuity in BV

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...

A new L1-lower semicontinuity result

The aim of this work is to prove a chain rule and an L1-lower semicontinuity theorems for integral functional defined on BV (Ω). Moreover we apply this result in order to obtain new relaxation and Γ-convergence result without any coerciveness and any continuity assumption of the integrand f(x, s, p) with respect to the variable s. Sunto. L’obiettivo di questo lavoro é quello di dimostrare una n...

Lower semicontinuity for parametric set-valued vector equilibrium-like problems

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...