On prouve la Cheeger-différentiabilité des applications de l'espace de Hajlasz lorsque est un certain type d'espace métrique mesuré (les espaces ) et lorsque appartient à une certaine classe d'espaces de Banach (les espaces de Banach GFDA ou plus généralement, les espaces de Banach RNP) pour un paramètre assez grand relié à la constante de doublement de la mesure supportée par . La classe d'espace de Banach considérée est la plus large possible et la dépendance de en la constante de doublement de la mesure supportée par est optimale.
The Cheeger-differentiability of maps belonging to Hajlasz spaces is proved. The assumption are rather simple. The metric space is assumed to support a doubling measure for which a Poincaré inequality is satisfied. The target space is assumed to be a RNP Banach space. Finally, the parameter must be large enough compared to the doubling constant of the measure (a precise and optimal dependance is given by the way). Notice that the class of Banach spaces considered is the largest possible (it gives a new characterization of RNP in term of Cheeger-differentiability).
Mots-clés : Inégalites de Poincaré, mesure doublante, espaces de Hajlasz-Sobolev
Keywords: Poincaré inequality, doubling measure, Hajlasz-Sobolev spaces
@article{BSMF_2014__142_1_63_0,
author = {Munnier, Vincent},
title = {Cheeger-diff\'erentiabilit\'e d'applications de certains espaces de {Sobolev}},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {63--93},
year = {2014},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {142},
number = {1},
doi = {10.24033/bsmf.2659},
mrnumber = {3248723},
zbl = {1304.30076},
language = {fr},
url = {https://www.numdam.org/articles/10.24033/bsmf.2659/}
}
TY - JOUR AU - Munnier, Vincent TI - Cheeger-différentiabilité d'applications de certains espaces de Sobolev JO - Bulletin de la Société Mathématique de France PY - 2014 SP - 63 EP - 93 VL - 142 IS - 1 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2659/ DO - 10.24033/bsmf.2659 LA - fr ID - BSMF_2014__142_1_63_0 ER -
%0 Journal Article %A Munnier, Vincent %T Cheeger-différentiabilité d'applications de certains espaces de Sobolev %J Bulletin de la Société Mathématique de France %D 2014 %P 63-93 %V 142 %N 1 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2659/ %R 10.24033/bsmf.2659 %G fr %F BSMF_2014__142_1_63_0
Munnier, Vincent. Cheeger-différentiabilité d'applications de certains espaces de Sobolev. Bulletin de la Société Mathématique de France, Tome 142 (2014) no. 1, pp. 63-93. doi: 10.24033/bsmf.2659
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