Differential Harnack inequalities for linear parabolic equations
Paul W. Y. Lee
TL;DR
This paper establishes matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and Kähler manifolds, advancing the understanding of their geometric and analytic properties.
Contribution
It introduces new differential Harnack inequalities applicable to linear parabolic equations on complex and Riemannian manifolds, extending previous scalar results.
Findings
Proved matrix differential Harnack inequalities on Riemannian manifolds.
Established scalar differential Harnack inequalities on Kähler manifolds.
Enhanced the theoretical framework for analyzing linear parabolic equations in geometric contexts.
Abstract
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and K\"ahler manifolds.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems