  We study the coupled equations describing fluctuations of scalars and the
metric about background solutions of N=8 gauged supergravity which are dual to
boundary field theories with renormalization group flow. For the case of a kink
solution with a single varying scalar, we develop a procedure to decouple the
equations, and we solve them in particular examples. However, difficulties
occur in the calculation of correlation functions from the fluctuations,
presumably because the AdS/CFT correspondence has not yet been properly
implemented in the coupled scalar-gravity sector. Some new examples of
correlators of operators dual to simpler uncoupled bulk scalars are given and
are satisfactory. As byproducts of our study we make some observations relevant
to the stability of domain walls in the brane-world scenario and to the
Hamilton-Jacobi formulation of holographic RG flows.
