On the role of lower bounds in characterizations of weak lower semicontinuity of multiple integrals

Abstract We study weak lower semicontinuity of integral functionals in W 1,p under standard p-growth conditions, with integrands whose negative part may have p-growth as well. A characterization is obtained which, besides quasiconvexity of the integrand, involves a second condition that in general is weaker than boundary quasiconvexity at zero as defined by Ball and Marsden, although for p-homogeneous integrands, it reduces to the latter.

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