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NEW CONVEXITY CONDITIONS IN THE CALCULUS OF VARIATIONS AND COMPENSATED COMPACTNESS THEORY

We consider the lower semicontinuous functional of the form where u satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar's Λ -convexity condition for the integrand f extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions apply to quasiconvex functions.