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: firstname.lastname@example.org
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
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