A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations

作者：Lin Jessica^*

来源：Communications in Partial Differential Equations, 2015, 40(9): 1688-1704.

DOI：10.1080/03605302.2014.985795

• Regularity for fully nonlinear uniformly parabolic equations
• 35K55

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.

• 出版日期2015-9-2