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Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization

Robert LiptonTadele Mengesha — 2012

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We examine the composition of the norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the ...

Representation formulas for norms of weakly convergent sequences of gradient fields in homogenization

Robert LiptonTadele Mengesha — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

We examine the composition of the norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds...

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