  One method available to prove the Schauder estimates is Neil Trudinger's
method of mollification. In the case of second order elliptic equations, the
method requires little more than mollification and the solid mean value
inequality for subharmonic functions. Our goal in this article is show how the
mean value property of subsolutions of the heat equation can be used in a
similar fashion as the solid mean value inequality for subharmonic functions in
Trudinger's original elliptic treatment, providing a relatively simple
derivation of the interior Schauder estimate for second order parabolic
equations.
