On the lower semicontinuity of supremal functional under differential constraints

Nadia Ansini, Francesca Prinari

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the weak∗ lower semicontinuity of functionals of the form (Equation Presented), where Ω ⊂ ℝis a bounded open set, V ∈ L (Ω;double-struck MdxN)∩Ker A and A is a constant-rank partial differential operator. The notion of A-Young quasiconvexity, which is introduced here, provides a sufficient condition when f(x, ·) is only lower semicontinuous. We also establish necessary conditions for weak∗ lower semicontinuity. Finally, we discuss the divergence and curl-free cases and, as an application, we characterise the strength set in the context of electrical resistivity.

Original languageEnglish
Pages (from-to)1053-1075
Number of pages23
JournalEsaim-Control Optimisation and Calculus of Variations
Volume21
Issue number4
Early online date24 Jun 2015
DOIs
Publication statusPublished - Oct 2015

Keywords

  • A-quasiconvexity
  • L<sup>p</sup>-approximation
  • Lower semicontinuity
  • Supremal functionals
  • Γ-convergence

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