  We consider heterostructures obtained by stacking layers of two s-wave
superconductors with significantly different coupling strengths, respectively
in the weak- and strong-coupling regimes. The weak- and strong-coupling
superconductors are chosen with similar critical temperatures for bulk systems.
Using dynamical mean-field theory methods, we find an ubiquitous enhancement of
the superconducting critical temperature for all the heterostructures where a
single layer of one of the two superconductors is alternated with a thicker
multilayer of the other. Two distinct physical regimes can be identified as a
function of the thickness of the larger layer: (i) an inherently inhomogeneous
superconductor characterized by the properties of the two isolated bulk
superconductors where the enhancement of the critical temperature is confined
to the interface and (ii) a bulk superconductor with an enhanced critical
temperature extending to the whole heterostructure. We characterize the
crossover between these regimes in terms of the competition between two length
scales connected with the proximity effect and the pair coherence.
