Volume 27, 2021
|Number of page(s)||15|
|Published online||21 December 2021|
Lower semi-continuity for 𝒜-quasiconvex functionals under convex restrictions
Institute of Applied Analysis, Ulm University,
* Corresponding author: email@example.com
Accepted: 30 November 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.
Mathematics Subject Classification: 49J45 / 35E10 / 35Q35
Key words: Convex sets / 𝒜-quasiconvexity / 𝒜-free / lower semi-continuity / Young measures / potentials / calculus of variations
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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