  We give some theoretical as well as computational results on Laplace and
Maxwell constants. Besides the classical de Rham complex we investigate the
complex of elasticity and the complex related to the biharmonic equation and
general relativity as well using the general functional analytical concept of
Hilbert complexes. We consider mixed boundary conditions and bounded Lipschitz
domains of arbitrary topology. Our numerical aspects are presented by examples
for the de Rham complex in 2D and 3D which not only confirm our theoretical
findings but also indicate some interesting conjectures.
