Quadratic expansions and partial regularity for fully nonlinear uniformly parabolic equations

Abstract

For a parabolic equation associated to a uniformly elliptic operator, we obtain a $W^{3,\epsilon }$ 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 $W^{2,\epsilon }$ 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 $\epsilon$ less than that of the ambient space, where the constant $\epsilon >0$ depends only on the dimension and the ellipticity.

34 pages, 2 figures. arXiv admin note: text overlap with arXiv:1103.3677 by other authors

Cited by in corpus (2)

• Global $W^{2,\delta }$ estimates for a type of singular fully nonlinear elliptic equations
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