G-convergence and the weak operator topology |
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| Authors: | Marcus Waurick |
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| Institution: | University of Bath, Claverton Down, Department of Mathematical Sciences, BA2 7AY, 4 West, Room 5.18 |
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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. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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