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The paper is devoted to special a priori estimates and Fredholm property of differential operators acting in anisotropic Sobolev spaces in ℝn. Necessary conditions for a priori estimates in terms of the symbol of an operator are obtained. Under appropriate conditions imposed on the coefficients, a priori estimates are obtained in the corresponding...
The paper investigates the index of some linear, differential, semielliptic operators with variable coefficients of a special
form in ℝ
n
. In particular, additional conditions on the symbol are found that render the index finite. The operators are considered
in the weighted Sobolev spaces.