  We describe a general strategy for the verification of variational source
condition by formulating two sufficient criteria describing the smoothness of
the solution and the degree of ill-posedness of the forward operator in terms
of a family of subspaces. For linear deterministic inverse problems we show
that variational source conditions are necessary and sufficient for convergence
rates slower than the square root of the noise level. A similar result is shown
for linear inverse problems with white noise. If the forward operator can be
written in terms of the functional calculus of a Laplace-Beltrami operator,
variational source conditions can be characterized by Besov spaces. This is
discussed for a number of prominent inverse problems.
