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arXiv · 1909.11543

Lower Semi-Continuity for $\mathcal A$-Quasiconvex Functionals under Convex Restrictions

Jack W. D. Skipper·Emil Wiedemann
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Abstract

We show weak lower semi-continuity of functionals assuming the new notion of a "convexly constrained" $\mathcal A$-quasiconvex integrand. We assume $\mathcal A$-quasiconvexity only for functions defined on a set $K$ which is convex. Assuming this and sufficient integrability of the sequence we show that the functional is still (sequentially) weakly lower semi-continuous along weakly convergent "convexly constrained" $\mathcal A$-free sequences. In a motivating example, the integrand is $-\det^{\frac{1}{d-1}}$ and the convex constraint is positive semi-definiteness of a matrix field.

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Jack W. D. Skipper, Emil Wiedemann. 2019-09-25. Lower Semi-Continuity for $\mathcal A$-Quasiconvex Functionals under Convex Restrictions. https://arxiv.org/abs/1909.11543

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