Sobolev spaces on multiple cones
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 707-733.

The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from n . The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.

L’objet de cet article est de décrire le comportement de certaines familles d’espaces de Sobolev en ce qui concerne la densité des fonctions régulières, l’interpolation, les propriétés d’extension et de restriction. Les méthodes combinent de façon intéressante les inégalités de Poincaré et des inégalités de type Hardy.

DOI: 10.5802/afst.1264
Auscher, P. 1; Badr, N. 2

1 Paris-Sud, Laboratoire de Mathématiques, UMR 8628, Orsay, F-91405 ; CNRS, Orsay, F-91405
2 Université de Lyon; CNRS; Université Lyon 1, Institut Camille Jordan, 43 boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France
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Auscher, P.; Badr, N. Sobolev spaces on multiple cones. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 707-733. doi : 10.5802/afst.1264. http://archive.numdam.org/articles/10.5802/afst.1264/

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