Volume 24, Number 4, October–December 2018
|Page(s)||1605 - 1624|
|Published online||10 December 2018|
Closed 𝓐-p Quasiconvexity and Variational Problems with Extended Real-Valued Integrands
Mathematical Institute, University of Oxford,
Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road,
OX2 6GG, UK
* Corresponding author: email@example.com
Accepted: 8 September 2017
This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential constraint, to closed 𝓐-p quasiconvexity of the integrand. The lower semi-continuous envelope of relaxation is identified for continuous, but potentially extended real-valued integrands. We discuss the continuity assumption and show that when it is dropped our notion of quasiconvexity is still equivalent to lower semi-continuity of the integrand under an additional assumption on the characteristic cone of 𝓐.
Mathematics Subject Classification: 35E99 / 49J45
Key words: Closed A-p quasiconvexity / extended real-valued integrands / semi-continuity / Young measures / relaxation
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.