Γ-convergence and Sobolev norms

Abstract

We study a Γ-convergence problem related to a new characterization of Sobolev spaces W 1 , p ( R N ) ( p > 1 ) established in H.-M. Nguyen [H.-M. Nguyen, Some new characterizations of Sobolev spaces, J. Funct. Anal. 237 (2006) 689–720] and J. Bourgain and H.-M. Nguyen [J. Bourgain, H.-M. Nguyen, A new characterization of Sobolev spaces, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 75–80]. We can also handle the case p = 1 which was out of reach previously. To cite this article: H.-M. Nguyen, C. R. Acad. Sci. Paris, Ser. I 345 (2007).