  We reexamine the constraints on mixing between electron and muon or tau
neutrinos from shock-reheating and r-process nucleosynthesis in supernovae. To
this end neutrino flavor evolution is described by nonlinear equations
following from a quantum kinetic approach. This takes into account neutrino
forward scattering off the neutrino background itself. In contrast to other
claims in the literature it is shown that a sound self-consistent analytical
approximation can in the first place only be performed in the adiabatic limit
where phase terms are suppressed. In the cosmologically interesting mass range
below about $25\eV$ the resulting mixing parameter bounds are between one and
two orders of magnitude less restrictive than limits neglecting neutrino
contributions. Extensions to the non-adiabatic regime derived in the literature
usually neglect coherence effects from phases. To check their importance
numerical simulations of the evolution equations were performed in this regime.
They indicate that analytical approximations for the flavor conversion
efficiencies can indeed be extended by neglecting phase terms. This allows more
stringent bounds similar to the ones derived in earlier work. These bounds
depend to some extent on the adopted supernova model and tend to be somewhat
less restrictive in the mixing angle but simultaneously extend to smaller
mixing masses compared to limits neglecting the neutrino induced potential.
