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We study properties of the functional $$\begin{array}{c}\hfill {ℱ}_{\mathrm{loc}}(u,\Omega ):=\underset{\left(u_j\right)}{inf}\left\{\underset{j\to \infty }{lim\; inf}{\int }_{\Omega }f\left(\nabla u_j\right)x\left|\begin{array}{cc}& \left(u_j\right)\subset W_{\mathrm{loc}}^{1,r}\left(\Omega ,\right)\hfill \\ & u_{j}u\mathrm{in}\left(\Omega ,\right)\hfill \end{array}\right.\right\},\end{array}$$ F loc ( u,Ω ) : = inf ( u j ) lim inf j → ∞ ∫ Ω f ( ∇ u j ) d x , whereu ∈ BV(Ω;R ^N ), and f:R ^{N × n} → R is continuous and satisfies 0 ≤ f(ξ) ≤

A lower semicontinuity result in is obtained for quasiconvex integrals with subquadratic growth. The key steps in this proof involve obtaining boundedness properties for an extension operator, and a precise blow-up technique that uses fine properties of Sobolev maps. A similar result is obtained by Kristensen in [7 (1998) 249–261], where there are weaker asssumptions on convergence but the integral needs to satisfy a stronger growth condition.