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

2013/05/31 by Jessica Lin, Lin, Jessica
Computer Science · Mathematics · #35K55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1305.7499

openalex publication_date 2013/05/31 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

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.

Citations

• On a result of Jessica Lin

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