Elsevier, Journal of Mathematical Analysis and Applications, 2(360), p. 495-502, 2009
DOI: 10.1016/j.jmaa.2009.06.068
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In this work we are going to prove the functional J defined by is weakly lower semicontinuous in W1,p(Ω) if and only if W is separately convex. We assume that Ω is an open set in Rn and W is a real-valued continuous function fulfilling standard growth and coerciveness conditions. The key to state this equivalence is a variational result established in terms of Young measures.