  Neutrino induced reactions are a basic ingredient in astrophysical processes
like star evolution. The existence of neutrino oscillations affects the rate of
nuclear electroweak decays which participates in the chain of events that
determines the fate of the star. Among the processes of interest, the
production of heavy elements in core-collapse supernovae is strongly dependent
upon neutrino properties, like the mixing between different species of
neutrinos. In this work we study the effects of neutrino oscillations upon the
electron fraction as a function of the neutrino mixing parameters, for two
schemes: the $1+1$ scheme (one active neutrino and one sterile neutrino) and
the $2+1$ scheme (two active neutrinos and one sterile neutrino). We have
performed this analysis considering a core-collapse supernovae and determined
the physical conditions needed to activate the nuclear reaction chains involved
in the r-process. We found that the interactions of the neutrinos with matter
and among themselves and the initial amount of sterile neutrinos in the
neutrino-sphere might change the electron fraction, therefore affecting the
onset of the r-process. We have set constrains on the active-sterile neutrino
mixing parameters. They are the square-mass-difference $\Delta m^2_{14} $, the
mixing angle $\sin^2 2\theta_{14}$, and the hindrance factor $\xi_s $ for the
occupation of sterile neutrinos. The calculations have been performed for
different values of $X_{\alpha}$, which is the fraction of $\alpha$-particles.
For $X_{\alpha}=0$ the r-process is taking place if $\Delta m^2_{14} \geq 2 \,
{\rm eV}^2 $, $\sin^2 2\theta_{14} < 0.8 $ and $\xi_s < 0.5$. For larger values
of $X_{\alpha}$ the region of parameters is strongly reduced. The present
results are compared to results available in the literature.
