TY - JOUR
T1 - Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank
AU - Xu , Lu
AU - Yan , Bianlian
JO - Analysis in Theory and Applications
VL - 2
SP - 147
EP - 162
PY - 2023
DA - 2023/06
SN - 39
DO - http://doi.org/10.4208/ata.OA-2021-0048
UR - https://global-sci.org/intro/article_detail/ata/21820.html
KW - Harnack inequalities, parabolic equations, microscopic convexity.
AB - <p style="text-align: justify;">We study microscopic convexity properties of convex solutions of fully nonlinear 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.</p>