We give a new proof of sequential weak* lower semicontinuity in BV(Ω;Rm) for integral functionals of the form F(u) := ∫

We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of compensated compactness, the latter represe...

A natural question in mathematical general relativity is how the ADM mass behaves as a functional on space of asymptotically flat 3-manifolds nonnegative scalar curvature. In previous results, lower semicontinuity has been established by first-named author for pointed $$C^2$$ convergence, and more generally both authors $$C^0$$ convergence (all Cheeger-Gromov sense). this paper, we show behavio...

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 $k$...

The concept of the lower limit for vector-valued mappings is the main focus of this work. We first introduce a new definition of adequate lower and upper level sets for vector-valued mappings and establish some of their topological and geometrical properties. Characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define the concept of vector lower limit,...