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Elliptic operators with singular coefficients. (English. Russian original) Zbl 1163.35355
Math. Notes 71, No. 5, 721-723 (2002); translation from Mat. Zametki 71, No. 5, 790-793 (2002).
The author considers strongly elliptic operators of the form
\[ L= \sum_{|\alpha|,|p|\leq m} D^\alpha C_{\alpha,\beta}(x) D^\beta \]
under the assumption that \(x\in\mathbb R^n\) and the coefficients \(C_{\alpha,\beta}\) are singular functions. The main goal of this paper is to find sufficient conditions on the coefficients for the operator \(L\) to be well-defined. Moreover, the author obtains results on the approximation in the sense of uniform resolvent convergence of the operators under consideration by operators of the same form but with smooth coefficients.
35J30 Higher-order elliptic equations
35P05 General topics in linear spectral theory for PDEs
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