Displaying similar documents to “Curl bounds Grad on SO(3)”

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...

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, a W - 1 , N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of  ℝ N . The proof is based partially on the Strauss inequality [Strauss, (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the...