We study points of density of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.
Dans cet article nous étudions la structure de l’ensemble des points avec densité pour les ensemble de périmètre fini dans un espace gaussien infini-dimensionnel. Nous démontrons que, comme dans le cas de dimension finie, la mesure de surface est concentrée sur cet ensemble de points. Ici, la définition de points avec densité est donnée en utilisant le comportement ponctuel du semigroupe de Ornstein-Uhlembeck.
@article{AFST_2011_6_20_2_407_0,
author = {Luigi Ambrosio and Alessio Figalli},
title = {Surface measures and convergence of the {Ornstein-Uhlenbeck} semigroup in {Wiener} spaces},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {407--438},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 20},
number = {2},
year = {2011},
doi = {10.5802/afst.1297},
mrnumber = {2847889},
zbl = {1228.60063},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1297/}
}
TY - JOUR AU - Luigi Ambrosio AU - Alessio Figalli TI - Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 407 EP - 438 VL - 20 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1297/ DO - 10.5802/afst.1297 LA - en ID - AFST_2011_6_20_2_407_0 ER -
%0 Journal Article %A Luigi Ambrosio %A Alessio Figalli %T Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 407-438 %V 20 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1297/ %R 10.5802/afst.1297 %G en %F AFST_2011_6_20_2_407_0
Luigi Ambrosio; Alessio Figalli. Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 2, pp. 407-438. doi : 10.5802/afst.1297. https://afst.centre-mersenne.org/articles/10.5802/afst.1297/
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