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The multidimensional Weyl theorem and covering families. (English. Russian original) Zbl 1042.47033

Math. Notes 73, No. 1, 36-45 (2003); translation from Mat. Zametki 73, No. 1, 38-48 (2003).
The essential self-adjointness of elliptic operators of the form \(M=(\nabla -ib(x))^*(A(x)(\nabla -ib(x)u)+q(x)u\) in \(L_2(G)\) is studied. Here \(G\) is an open set in \(\mathbb{R}^n\), \(A(x)\) is a positive symmetric matrix function, \(b(x)\) is an \(n\)-component vector-function with real components, and \(q(x)\) is a real function satisfying the condition \(q(x)\geq \text{const.}\), \(x\in G\).

MSC:

47F05 General theory of partial differential operators
35J15 Second-order elliptic equations
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