  In this article, we prove the local $C^{0,\alpha}$ regularity and provide
$C^{0,\alpha}$ estimates for viscosity solutions of fully nonlinear, possibly
degenerate, elliptic equations associated to linear or nonlinear Neumann type
boundary conditions. The interest of these results comes from the fact that
they are indeed regularity results (and not only a priori estimates), from the
generality of the equations and boundary conditions we are able to handle and
the possible degeneracy of the equations we are able to take in account in the
case of linear boundary conditions.
