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

A proof of the parabolic Schauder estimates using Trudinger's method and the mean value property of the heat equation