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MR1484656 (98k:35033) 35J15 (47F05 58G03)
Brusentsev, A. G. On the essential selfadjointness of second-order semibounded elliptic operators that are not subject to the condition of the completeness of the Riemannian manifold. (Russian) Mat. Fiz. Anal. Geom. 2 (1995), no. 2, 152--167.
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