Geodesic
Near boundary behavior of elliptic operator potential garanteeing its essential self-adjointness
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998), pp. 149-165.

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For the class of elliptic operations in space $L_2(G)$ ($G$ is an arbitrary open set in $R^N$), containing the Schrödinger operator with electromagnetic potential, conditions are obtained on near boundary behavior of the coefficients under which the operator was essential self-adjoint on $C_0^\infty(G)$. The closeness of the sufficient conditions derived to the necessary ones is discussed by examples. 
@article{JMAG_1998_5_a1,
     author = {A. G. Brusentsev},
     title = {Near boundary behavior of elliptic operator potential garanteeing its essential self-adjointness},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {149--165},
     publisher = {mathdoc},
     volume = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1998_5_a1/}
}
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A. G. Brusentsev. Near boundary behavior of elliptic operator potential garanteeing its essential self-adjointness. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (1998), pp. 149-165. http://geodesic.mathdoc.fr/item/JMAG_1998_5_a1/