G-convergence and the weak operator topology

Marcus Waurick

doi:10.1002/pamm.201610430

G-convergence and the weak operator topology

Marcus Waurick

Mathematics And Statistics

Research output: Contribution to journal › Conference Contribution › peer-review

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 language	English
Pages (from-to)	883-884
Number of pages	2
Journal	Proceedings in Applied Mathematics and Mechanics, PAMM
Volume	16
Issue number	1
DOIs	https://doi.org/10.1002/pamm.201610430
Publication status	Published - 25 Oct 2016

Keywords

bounded sequence
G-convergence
weak operator topology

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10.1002/pamm.201610430

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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

KW - G-convergence

KW - weak operator topology

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DO - 10.1002/pamm.201610430

M3 - Conference Contribution

SN - 1617-7061

VL - 16

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JO - Proceedings in Applied Mathematics and Mechanics, PAMM

JF - Proceedings in Applied Mathematics and Mechanics, PAMM

IS - 1

ER -

G-convergence and the weak operator topology

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