Geodesic
On the negative spectrum of an elliptic operator
Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 155-177

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New estimates are given for the number of points in the negative spectrum for an elliptic operator or arbitrary order. These estimates generalize and refine the well-known results of Rozenblyum, Lieb, Cwikel, the authors, and others. The proofs have a simple geometric character, and are based on uncomplicated dimensionless imbedding theorems. Also given are results for degenerate elliptic operators, for operators in a domain that contracts or expands in a definite way at infinity, and so on. Theorem 10 gives conditions under which the essential spectrum of an operator contains infinitely many points. 
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Yu. V. Egorov; V. A. Kondrat'ev. On the negative spectrum of an elliptic operator. Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 155-177. http://geodesic.mathdoc.fr/item/SM_1991_69_1_a9/