HIGHLIGHTS
SUMMARY
Within the weak theory in the space (G)SBV of_(generalized) special functions of bounded variation, the problem of finding sufficient conditions for the lower semicontinuity of functionals like (1.1) has been addressed e_g. The function r 7→ gε (x, r) is continuously differentiable in Rd for Hd-1 -a.e. x ∈ Rd, |∇r gε (x, r)|=|(g * ∇ρε )(x, r)| ≤ M, and by_(G30 ) |∇r gε (x, r) - ∇r gε (x, s)| ≤ C ω̃(|r - s|) for all r, s ∈ Rd and Hd-1 -a.e. x ∈ Rd. From (K3), for Hd-1 -a . . .
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