Abstract
A self-contained approach to lower semicontinuity and lower closure evolves from an extension of relaxed control theory, which is based on a central relative weak compactness criterion (called tightness) and relaxation in all but one variable. Two lower closure results for outer integral functionals with variable abstract time domain are developed. The first of these has a convexity condition for the integrand and generalizes all similar results in the literature. The second lower closure result is of a new kind; among other things, it implies a quite general version of Fatou's lemma in several dimensions.
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