Comptes Rendus
no. 12
Partial Differential Equations
Γ-convergence and Sobolev norms
[Γ-convergence et normes de Sobolev]

Présenté par : Haïm Brezis

Hoai-Minh Nguyen1
1 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 679-684.

On étudie un problème de Γ-convergence qui apparaît naturellement en liaison avec les travaux de H.-M. Nguyen [H.-M. Nguyen, Some new characterizations of Sobolev spaces, J. Funct. Anal. 237 (2006) 689–720], et J. Bourgain et 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] concernant des nouvelles caractérisations des espaces de Sobolev W1,p(RN) (p>1). On peut aussi traiter le cas p=1 qui était inaccessible précédemment.

We study a Γ-convergence problem related to a new characterization of Sobolev spaces W1,p(RN) (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.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.11.005
Hoai-Minh Nguyen 1

1 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA 
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Hoai-Minh Nguyen. Γ-convergence and Sobolev norms. Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 679-684. doi : 10.1016/j.crma.2007.11.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.005/

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[13] H.-M. Nguyen, Γ-convergence, Sobolev norms, and BV functions, in preparation

[14] H.-M. Nguyen, Some inequalities related to Sobolev norms, in preparation

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