PIRE - mathematics, mechanics, materials science

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

Publication 93

A Note on Two Scale Compactness for p = 1


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

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

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

Back to Publications