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

Autor:	Skipper, Jack W. D., Wiedemann, Emil
Rok vydání:	2019
Předmět:	Mathematics - Analysis of PDEs Mathematics - Functional Analysis 49J45
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages, Keywords: Convex Sets, $\mathcal A $-Quasiconvexity, $\mathcal A$-Free, Lower Semi-continuity, Young Measures, Potentials, and Calculus of Variations
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.11543 Zobrazit plný text záznamu View this record from Arxiv