Riesz-basis construction for second order elliptic problems with jump coefficients

We consider a Laplace type boundary value problem with a generally discontinuous diffusion coefficient. A domain decomposition technique is used to construct a Riesz basis that, when normalised w.r.t. the energy-norm, has Riesz constants that are bounded uniformly in the jumps. By extension operators, we construct a basis for a range of Sobolev spaces on a domain from corresponding bases on subdomains. The desired Riesz basis are uniformly stable in the diffusion coefficients.