  We establish new Hoelder and Lipschitz estimates for viscosity solutions of a
large class of elliptic and parabolic nonlinear integro-differential equations,
by the classical Ishii-Lions's method. We thus extend the Hoelder regularity
results recently obtained by Barles, Chasseigne and Imbert (2011). In addition,
we deal with a new class of nonlocal equations that we term mixed
integro-differential equations. These equations are particularly interesting,
as they are degenerate both in the local and nonlocal term, but their overall
behavior is driven by the local-nonlocal interaction, e.g. the fractional
diffusion may give the ellipticity in one direction and the classical diffusion
in the complementary one.
