Lower Semicontinuity for Integral Functionals in the Space of Functions of Bounded Deformation via Rigidity and Young Measures by

Lower Semicontinuity for Functions of Bounded Deformation via Rigidity and Young Measures

We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

A lower semicontinuity result in SBD for surface integral functionals of Fracture Mechanics

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.

Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics

We study nonlocal variational problems in Lp, like those that appear in peridynamics. The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions of either a convexity notion of the integrand, or a Jensen inequality for Young measures. Existence results, obtained through the direct ...

Lower Semicontinuity and Young Measures in BV Without Alberti's Rank-One Theorem by

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

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces