# Science at the triple point between mathematics, mechanics and materials science

## Publication 93

### A Note on Two Scale Compactness for p = 1

##### Authors:

Laura Bufford
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213, USA

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

##### Abstract:
In this paper the notion of two-scale convergence introduced by G. Nguetseng and G. Allaire is extended to the case of bounded sequences in $L^1(\Omega)$, where $\Omega$ is any open subset of $\mathbb{R}^N$. Three diff erent approaches will be considered: an adaptation of the method used in $L^p(\Omega)$ with $p > 1$, a measure-theoretic argument, and the periodic unfolding technique. Keywords: two-scale convergence, periodic integrals.
##### Get the paper in its entirety
14-CNA-004.pdf

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