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 . 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.
@article{AFST_2010_6_19_3-4_707_0,
author = {P. Auscher and N. Badr},
title = {Sobolev spaces on multiple cones},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {707--733},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 19},
number = {3-4},
year = {2010},
doi = {10.5802/afst.1264},
mrnumber = {2790816},
zbl = {1219.46031},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1264/}
}
TY - JOUR AU - P. Auscher AU - N. Badr TI - Sobolev spaces on multiple cones JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 707 EP - 733 VL - 19 IS - 3-4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1264/ DO - 10.5802/afst.1264 LA - en ID - AFST_2010_6_19_3-4_707_0 ER -
%0 Journal Article %A P. Auscher %A N. Badr %T Sobolev spaces on multiple cones %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 707-733 %V 19 %N 3-4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1264/ %R 10.5802/afst.1264 %G en %F AFST_2010_6_19_3-4_707_0
P. Auscher; N. Badr. 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. https://afst.centre-mersenne.org/articles/10.5802/afst.1264/
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