  We study Talenti's type symmetrization properties for solutions of linear
stationary and evolution problems. Our main result establishes the comparison
in norm between the solution of a problem and its symmetric version when
nonlocal diffusion defined through integrable kernels is replacing the usual
local diffusion defined by a second order differential operator. Using an
approximation argument, we recover, as a corollary of our results, the
classical Talenti's theorem. A novelty of our approach is that we replace the
measure geometric tools employed in Talenti's proof by the use of the Riesz's
rearrangement inequality, giving thus an alternative and somehow simpler proof
than Talenti's one.
