Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces

Luigi Ambrosio[1]; Alessio Figalli[2]

  • [1] Scuola Normale Superiore, p.za dei Cavalieri 7, I-56126 Pisa, Italy.
  • [2] The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, USA

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 2, page 407-438
  • ISSN: 0240-2963

Abstract

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We study points of density 1 / 2 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 1 / 2 is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.

How to cite

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Ambrosio, Luigi, and Figalli, Alessio. "Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces." Annales de la faculté des sciences de Toulouse Mathématiques 20.2 (2011): 407-438. <http://eudml.org/doc/219778>.

@article{Ambrosio2011,
abstract = {We study points of density $1/2$ 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 $1/2$ is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.},
affiliation = {Scuola Normale Superiore, p.za dei Cavalieri 7, I-56126 Pisa, Italy.; The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, USA},
author = {Ambrosio, Luigi, Figalli, Alessio},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {4},
number = {2},
pages = {407-438},
publisher = {Université Paul Sabatier, Toulouse},
title = {Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces},
url = {http://eudml.org/doc/219778},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Ambrosio, Luigi
AU - Figalli, Alessio
TI - Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 2
SP - 407
EP - 438
AB - We study points of density $1/2$ 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 $1/2$ is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.
LA - eng
UR - http://eudml.org/doc/219778
ER -

References

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