Elliptic operators with singular coefficients. (Q1810130)

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.