  Let q and v be symmetric sesquilinear forms such that v is a form
perturbation of q. Then we can associate a unique self-adjoint operator B to q+
v. Assuming that B has a gap (a, b) in the essential spectrum, we prove a
minimax principle for the eigenvalues of B in (a, b) using a suitable
orthogonal decomposition of the domain of q. This allows us to justify two
minimax characterisations of eigenvalues in the gap of three-dimensional Dirac
operators with electrostatic potentials having strong Coulomb singularities.
