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Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank

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We study microscopic convexity properties of convex solutions of fully non-linear parabolic equations under a structural condition introduced by Bian-Guan.We prove weak Harnack inequalities for the eigenvalues of the spatial Hessian of solutions and obtain the monotonicity of Hessian's rank with respect to time.

Harnack inequalitiesparabolic equationsmicroscopic convexity

Lu Xu、Bianlian Yan

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School of Mathematics,Hunan University,Changsha,Hunan 410082,China

NSFC

12171143

2023

10.4208/ata.OA-2021-0048

分析、理论与应用(英文版)
南京大学

分析、理论与应用(英文版)

影响因子：0.111
ISSN：1672-4070
年,卷(期)：2023.39(2)
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