%0 Journal Article
%T Quadratic expansions and partial regularity for fully nonlinear uniformly parabolic equations
%A Jean-Paul Daniel
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00526-014-0783-0
%X 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.
%U http://arxiv.org/abs/1309.3781v2