Geodesic
The Gauss-Ostrogradskii formula in infinite-dimensional space
Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 757-770 
O. V. Pugachev. The Gauss-Ostrogradskii formula in infinite-dimensional space. Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 757-770. http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/
@article{SM_1998_189_5_a5,
     author = {O. V. Pugachev},
     title = {The {Gauss-Ostrogradskii} formula in infinite-dimensional space},
     journal = {Sbornik. Mathematics},
     pages = {757--770},
     year = {1998},
     volume = {189},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/}
}
TY  - JOUR
AU  - O. V. Pugachev
TI  - The Gauss-Ostrogradskii formula in infinite-dimensional space
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 757
EP  - 770
VL  - 189
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/
LA  - en
ID  - SM_1998_189_5_a5
ER  - 
%0 Journal Article
%A O. V. Pugachev
%T The Gauss-Ostrogradskii formula in infinite-dimensional space
%J Sbornik. Mathematics
%D 1998
%P 757-770
%V 189
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1998_189_5_a5/
%G en
%F SM_1998_189_5_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of the present paper is to generalize the Gauss–Ostrogradskii theorem to an infinite-dimensional space $X$. On this space we consider not only Gaussian measures but a wider class of measures, differentiable along some Hilbert space continuously embedded in $X$. In the paper, a construction of a surface measure which employs ideas of the Malliavin calculus and the theory of Sobolev capacities is considered. It is a generalisation of the surface integration developed by Malliavin for the Wiener measure.

[1] Skorokhod A. V., Integrirovanie v gilbertovom prostranstve, Nauka, M., 1975

[2] Efimova E. I., Uglanov A. V., “Formula Grina na gilbertovom prostranstve”, Matem. sb., 119:2 (1982), 225–232 | MR | Zbl

[3] Efimova E. I., Uglanov A. V., “Formuly vektornogo analiza na banakhovom prostranstve”, Dokl. AN, 271:6 (1983), 1302–1306 | MR

[4] Uglanov A. V., “Poverkhnostnye mery v banakhovom prostranstve”, Matem. sb., 110:2 (1979), 189–217 | MR | Zbl

[5] Uglanov A. V., “Poverkhnostnye integraly v lineinykh topologicheskikh prostranstvakh”, Dokl. AN, 344:4 (1995), 450–453 | MR | Zbl

[6] Airault H., Malliavin P., “Integration geometrique sur l'espace de Wiener”, Bull. Sci. Math. (2), 112 (1988), 3–52 | MR | Zbl

[7] Bogachev V. I., Gaussovskie mery, Nauka, M., 1997 | MR

[8] Bogachev V. I., “Differentiable measures and the Malliavin calculus”, J. Math. Sci., 87:5 (1997), 3577–3731 | DOI | MR | Zbl

[9] Röckner M., Schmuland B., “Tightness of general $C_{1,p}$ capacities on Banach space”, J. Funct. Anal., 108:1 (1992), 1–12 | DOI | MR | Zbl

[10] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR