S.Dolgov, B.N. Khoromskij, I.Oseledets, and E.E. Tyrtyshnikov. Low-rank tensor structure of solutions to elliptic problems with jumping coefficients.Journal of Computational Mathematics, 30(1):1423, 2012.

We study the separability properties of solutions to elliptic equations with piecewise constant coeffcients in R^d, d >2. The separation rank of the solution to diffusion equation with variable coefficients is presented

: Structured matrices, Elliptic operators, Poisson equation, Matrix approxima- tions, Low-rank matrices, Tensors, Canonical decomposition.

: http://www.global-sci.org/jcm/volumes/v30n1/pdf/301-14.pdf