2016•PAMMOpen access

G‐convergence and the weak operator topology

Marcus Waurick

Abstract

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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Key concepts: Bounded function, Operator (biology), Embedding, Mathematics, Topology (electrical circuits), Sequence (biology), Convergence (economics), Matrix (chemical analysis)