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

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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. 
@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},
     publisher = {mathdoc},
     volume = {262},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a13/}
}
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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/