Geodesic
A remark on essential self-adjointness of nonsemi-bounded elliptic operators in~$L_2(G)$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 234-244.

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Conditions are obtained for the general-type symmetric elliptic second-order operator $L$ in space $L_2(G)$ ($D_L=C_0^{\infty}(G)$, $G$ is an arbitrary open set in $R^n$)under which self-adjointness $\overline{L}$ follows from the essential self-adjointness of some semi-bounded elliptic operator. 
@article{JMAG_1999_6_a3,
     author = {A. G. Brusentsev},
     title = {A remark on essential self-adjointness of nonsemi-bounded elliptic operators in~$L_2(G)$},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {234--244},
     publisher = {mathdoc},
     volume = {6},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_a3/}
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A. G. Brusentsev. A remark on essential self-adjointness of nonsemi-bounded elliptic operators in~$L_2(G)$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 234-244. http://geodesic.mathdoc.fr/item/JMAG_1999_6_a3/