Publication 14-CNA-004
**A Note on Two Scale Compactness for $p=1$**

Laura Bufford

Department of Mathematical Sciences

Carnegie Mellon University, Pittsburgh, PA 15213, USA

lbufford@andrew.cmu.edu

Irene Fonseca

Department of Mathematical Sciences

Carnegie Mellon University, Pittsburgh, PA 15213, USA

fonseca@andrew.cmu.edu

**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 different 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.

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