Perturbative analysis of the divergent contributions to the Casimir energy

We investigate the divergence structure of the Casimir energy for the case that ?(x) and μ(x) are general functions ofx and of the frequency. The analysis is done in perturbation theory up to second order. The degree of divergence is found to be lowered by one unit if the usual approximation of sharp boundaries is relaxed. This introduces the inverse width of the boundary layer as another physical cutoff for the divergent integrals, besides the cutoffs related to retardation and spatial nonlocality of the dielectric response.