Geodesic
The operator rot in an arbitrary region of finite measure
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 227-230 
N. D. Filonov. The operator rot in an arbitrary region of finite measure. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 227-230. http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a13/
@article{ZNSL_1999_262_a13,
     author = {N. D. Filonov},
     title = {The operator rot in an arbitrary region of finite measure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {227--230},
     year = {1999},
     volume = {262},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a13/}
}
TY  - JOUR
AU  - N. D. Filonov
TI  - The operator rot in an arbitrary region of finite measure
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1999
SP  - 227
EP  - 230
VL  - 262
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a13/
LA  - ru
ID  - ZNSL_1999_262_a13
ER  - 
%0 Journal Article
%A N. D. Filonov
%T The operator rot in an arbitrary region of finite measure
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 227-230
%V 262
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a13/
%G ru
%F ZNSL_1999_262_a13

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The definition of the self-adjoint operator rot in an arbitrary region $\Omega\subset\mathbb R^3$ of finite measure is investigated. The spectrum of the operator is discrete. One can prove Weyl's asymptotic formula for the eigenvalues. Under an additional condition concerning the boundary of the region a remainder estimate can be obtained.