We have performed dielectric spectroscopy on polymer gels consisting of propylene carbonate (PC) mixed with a polymer, poly(methyl methacrylate) (PMMA). The compositions of the investigated systems range from pure PC via PC/PMMA mixtures to pure polymer. In the supercooled regime of all the mixed compositions a dielectric loss peak, attributed to the main alpha relaxation of PC, is observed. The main influence of the restriction on the dynamics of PC by the polymer matrix is an increasingly slower and broader alpha relaxation for higher polymer concentrations. We show that there are strong correlations between the shape of the relaxation function, the structural relaxation time, and the macroscopic viscosity. Large polymer-induced changes at the low-frequency side of the loss peak coincide with a moderate increase in the relaxation time and are attributed to spatial restriction imposed by the polymer on long-range motion of PC. Changes at the high-frequency side of the loss peak are shown to correlate with a dramatic increase of the relaxation time, which is attributed to a gradual increase of the number of PC molecules that are affected by the polymer. Furthermore, the temperature and polymer concentration dependencies of the shape and strength of the loss peak can quantitatively be explained by cooperativity effects of the dynamics in the supercooled solvent.