  For a parabolic equation associated to a uniformly elliptic operator, we
obtain a $W^{3, \varepsilon}$ estimate, which provides a lower bound on the
Lebesgue measure of the set on which a viscosity solution has a quadratic
expansion. The argument combines parabolic $W^{2,\varepsilon}$ estimates with a
comparison principle argument. As an application, we show, assuming the
operator is $C^1$, that a viscosity solution is $C^{2,\alpha}$ on the
complement of a closed set of Hausdorff dimension $\varepsilon$ less than that
of the ambient space, where the constant $\varepsilon>0$ depends only on the
dimension and the ellipticity.
