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A lower semicontinuity result in BV 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 (Calc. Var. Partial Differ. Equ. 7 (1998) 249-261), where there are weaker asssumptions on convergence but the integral needs to satisfy a stronger growth condition.

Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth