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arXiv · 1305.7499

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Fully Nonlinear Uniformly Parabolic Equations

Jessica Lin
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Abstract

This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a nonlinear, quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of the Fabes-Stroock estimate. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.

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Jessica Lin. 2014-05-05. A Quantitative Regularity Estimate for Nonnegative Supersolutions of Fully Nonlinear Uniformly Parabolic Equations. https://arxiv.org/abs/1305.7499

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