A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations |
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Authors: | Jessica Lin |
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Affiliation: | Department of Mathematics , University of Wisconsin-Madison , Madison , Wisconsin , USA |
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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 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 a reverse Holder inequality. 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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Keywords: | Regularity for fully nonlinear uniformly parabolic equations |
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