Abstract
We prove theorems on the lower semicontinuity and integral representations of the lower semicontinuous envelopes of integral functionals with integrands L of fast growth: c1G(|Du|) + c2 ≤ L ≤ c3G(|Du|) + c4 with c3 ≥ c1 > 0 and G : [0, ∞[→ [0, ∞[ is an increasing convex function such that vG′ (v)/G(v) → ∞ as v → ∞ and is increasing for large v. Repeating the results for the case of the standard growth (G(⋅) = |⋅|p) the quasiconvexity of integrands characterizes the lower semicontinuity of integral functionals and their quasiconvexifications yield the integral functionals that are lower semicontinuous envelopes.
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