Elliptic operators with singular coefficients. (English. Russian original) Zbl 1163.35355

Neĭman-zade, M. I.

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.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

35J30	Higher-order elliptic equations
35P05	General topics in linear spectral theory for PDEs

Keywords:

elliptic operator; uniform resolvent convergence; singular coefficient