Lower semi-continuity for A-quasiconvex functionals under convex restrictions - Skipper, Jack; Wiedemann, Emil (Esaim-Control Optimisation and Calculus of Variations, 2021)
We show weak lower semi-continuity of functionals assuming the new notion of a "convexly constrained"A-quasiconvex integrand. We assume 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"A-free sequences. In a motivating example, the integrand is - det1/d-1 and the convex constraint is positive semi-definiteness of a matrix field.
CRIS-Team Scopus Importer:2023-01-17
Keywords: A-free; A-quasiconvexity; Calculus of variations; Convex sets; Lower semi-continuity; Potentials; Young measures