Displaying similar documents to “Estimate of the pressure when its gradient is the divergence of a measure. Applications”

Curl bounds Grad on SO(3)

Patrizio Neff, Ingo Münch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let F p GL ( 3 ) be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form Curl [ F p ] · ( F p ) T applied to rotations controls the gradient in the sense that pointwise R C 1 ( 3 , SO ( 3 ) ) : Curl [ R ] · R T 𝕄 3 × 3 2 1 2 D R 27 2 . This result complements rigidity results [Friesecke, James and Müller, (2002) 1461–1506; John, (1961) 391–413; Reshetnyak, (1967) 631–653)] as well as an associated linearized theorem saying...

Is it wise to keep laminating?

Marc Briane, Vincenzo Nesi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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 [, to appear]. In two dimensions it holds true for any microgeometry as a corollary of the work in Alessandrini and Nesi [ (2001) 155-171]. We use this property of laminates to prove...