  For QFTs in AdS the boundary correlation functions remain conformal even if
the bulk theory has a scale. This allows one to constrain RG flows with
numerical conformal bootstrap methods. We apply this idea to flows between
two-dimensional CFTs, focusing on deformations of the tricritical and ordinary
Ising model. We provide non-perturbative constraints for the boundary
correlation functions of these flows and compare them with conformal
perturbation theory in the vicinity of the fixed points. We also reproduce a
completely general constraint on the sign of the $T\bar T$ deformation in two
dimensions.
