G‐convergence and the weak operator topology. Issue 1 (25th October 2016) - Waurick, Marcus
Abstract: We show that a bounded sequence ( a n ) n of symmetric d × d ‐matrix valued functions is G ‐convergent if and only if ((ι ∗︁ a n ι) −1 ) n converges in the weak operator topology. Here ι: R (grad0 ) ↪ L 2 (Ω) d denotes the (canonical) embedding from the range of the weak gradient grad0 defined on H 1 0 (Ω) into L 2 (Ω) d, where Ω ⊆ ℝ d is open and bounded. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)