A note on two scale compactness for p=1p = 1

  • Laura Bufford

    Carnegie Mellon University, Pittsburgh, USA
  • Irene Fonseca

    Carnegie Mellon University, Pittsburgh, United States


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 L1(Ω)L^1(\Omega), where Ω\Omega is any open subset of RN\mathbb{R}^N. Three different approaches will be considered: an adaptation of the method used in Lp(Ω)L^p(\Omega) with p>1p>1, a measure-theoretic argument, and the periodic unfolding technique.

Cite this article

Laura Bufford, Irene Fonseca, A note on two scale compactness for p=1p = 1. Port. Math. 72 (2015), no. 2/3, pp. 101–117

DOI 10.4171/PM/1959