G-convergence and the weak operator topology

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.
LanguageEnglish
Pages883-884
Number of pages2
JournalProceedings in Applied Mathematics and Mechanics, PAMM
Volume16
Issue number1
DOIs
Publication statusPublished - 25 Oct 2016

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G-convergence
Mathematical operators
Topology
Operator
Gradient
If and only if
Denote
Converge
Range of data

Keywords

  • bounded sequence
  • G-convergence
  • weak operator topology

Cite this

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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.",
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G-convergence and the weak operator topology. / Waurick, Marcus.

In: Proceedings in Applied Mathematics and Mechanics, PAMM, Vol. 16, No. 1, 25.10.2016, p. 883-884.

Research output: Contribution to journalConference Contribution

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N2 - 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.

AB - 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.

KW - bounded sequence

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KW - weak operator topology

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M3 - Conference Contribution

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JF - Proceedings in Applied Mathematics and Mechanics, PAMM

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