G-convergence and the weak operator topology

Marcus Waurick

Research output: Contribution to journalConference Contribution

Abstract

We show that a bounded sequence (an)n of symmetric d × d-matrix valued functions is G-convergent if and only if ((ι∗anι)−1 )n converges in the weak operator topology. Here ι: R(grad0) ↪ L2(Ω)d denotes the (canonical) embedding from the range of the weak gradient grad0 defined on H10(Ω) into L2(Ω)d, where Ω ⊆ ℝd is open and bounded.
Original languageEnglish
Pages (from-to)883-884
Number of pages2
JournalProceedings in Applied Mathematics and Mechanics, PAMM
Volume16
Issue number1
DOIs
Publication statusPublished - 25 Oct 2016

Keywords

  • bounded sequence
  • G-convergence
  • weak operator topology

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