Abstract
A necessary and sufficient condition for the W1, p-quasi-convexity of integrands to imply the lower semicontinuity of the corresponding integral functionals with respect to the weak convergence of sequences in W1, p is obtained. It is shown that the absence of the Lavrent’ev phenomenon in minimization problems with linear boundary data is sufficient, under a minor technical assumption, for the lower semicontinuity of integral functionals with quasi-convex integrands.
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