Geodesic
De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 361-371

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

In his classical monograph Variétés Différentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an $N$-function $\Phi$ is $\Delta_2$-regular then the $L_\Phi$-cohomology of a Riemannian manifold can be calculated with the use of smooth $L^\Phi$-forms.
Keywords: Riemannian manifold, differential form, de Rham regularization operator, Orlicz space, operator of exterior derivation, $L_\Phi$-cohomology. 
@article{SEMR_2015_12_a82,
     author = {Ya. A. Kopylov and R. A. Panenko},
     title = {De {Rham} regularization operators in {Orlicz} spaces of differential forms on {Riemannian} manifolds},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {361--371},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a82/}
}
TY  - JOUR
AU  - Ya. A. Kopylov
AU  - R. A. Panenko
TI  - De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 361
EP  - 371
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a82/
LA  - en
ID  - SEMR_2015_12_a82
ER  - 
%0 Journal Article
%A Ya. A. Kopylov
%A R. A. Panenko
%T De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 361-371
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a82/
%G en
%F SEMR_2015_12_a82
Ya. A. Kopylov; R. A. Panenko. De Rham regularization operators in Orlicz spaces of differential forms on Riemannian manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 361-371. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a82/