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Is it wise to keep laminating?

Marc Briane, Vincenzo Nesi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the corrector matrix P ε  to the conductivity equations. We show that if P ε  converges weakly to the identity, then for any laminate det P ε 0 at almost every point. This simple property is shown to be false for generic microgeometries if the dimension is greater than two in the work Briane et al. [Arch. Ration. Mech. Anal., to appear]. In two dimensions it holds true for any microgeometry as a corollary of the work in Alessandrini and Nesi [Arch. Ration. Mech. Anal.158 (2001) 155-171]. We use this...

Is it wise to keep laminating ?

Marc Briane, Vincenzo Nesi (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We study the corrector matrix P ϵ to the conductivity equations. We show that if P ϵ converges weakly to the identity, then for any laminate det P ϵ 0 at almost every point. This simple property is shown to be false for generic microgeometries if the dimension is greater than two in the work Briane et al. [Arch. Ration. Mech. Anal., to appear]. In two dimensions it holds true for any microgeometry as a corollary of the work in Alessandrini and Nesi [Arch. Ration. Mech. Anal. 158 (2001) 155-171]. We use this...

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