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Volume 39, Issue 2
Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank

Lu Xu & Bianlian Yan

DOI: 10.4208/ata.OA-2021-0048

Anal. Theory Appl., 39 (2023), pp. 147-162.

Published online: 2023-06

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  • Abstract

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.

  • Keywords

Harnack inequalities, parabolic equations, microscopic convexity.

  • AMS Subject Headings

35K55, 35E10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-39-147, author = {Xu , Lu and Yan , Bianlian}, title = {Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {2}, pages = {147--162}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0048}, url = {http://global-sci.org/intro/article_detail/ata/21820.html} }
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 -

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.

Xu , Lu and Yan , Bianlian. (2023). Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank. Analysis in Theory and Applications. 39 (2). 147-162. doi:10.4208/ata.OA-2021-0048
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