Some approximation and regularity results for fully nonlinear parabolic equations

I will discuss some results on viscosity solutions of fully nonlinear parabolic equations associated to a uniformly elliptic operator. I derive an estimate which provides a lower bound on the Lebesgue measure of the set on which a viscosity solution has a quadratic expansion. I will present two applications: I get a partial regularity theorem, and in a joint work with Scott Armstrong, we also show how this can serve to study the rate of convergence for a broad class of schemes.