Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds. II: Integral curvature condition

DOI10.1016/j.na.2023.113426OpenAlexW4388509554MaRDI QIDQ6185363

Zhi-Hao Lu

Publication date: 8 January 2024

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2023.113426

zbMATH Keywords

nonlinear parabolic equationsheat flowODE systemdifferential Harnack inequalityelliptic estimateintegral curvature condition

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Semilinear parabolic equations (35K58) Positive solutions to PDEs (35B09) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

• Unnamed Item
• Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
• Logarithmic Harnack inequalities
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• Differential Harnack estimates for backward heat equations with potentials under the Ricci flow
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• A matrix Harnack estimate for the heat equation
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Relative volume comparison with integral curvature bounds
• The Li-Yau inequality and applications under a curvature-dimension condition
• Local Sobolev constant estimate for integral Ricci curvature bounds
• Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class
• Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions
• Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds
• Differential Harnack estimates for a nonlinear heat equation
• Differential Harnack estimates for time-dependent heat equations with potentials
• Li-Yau gradient bound for collapsing manifolds under integral curvature condition
• Liouville theorems for the ancient solution of heat flows
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Maximum Principles and Geometric Applications
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Convergence of riemannian manifolds with integral bounds on curvature. I
• Analysis and geometry on manifolds with integral Ricci curvature bounds. II
• Neumann Li-Yau gradient estimate under integral Ricci curvature bounds
• Harmonic Mappings of Riemannian Manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
• Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds. I: Bakry-Émery curvature bounded below
• Differential Harnack inequalities for semilinear parabolic equations on \(\mathrm{RCD}^{\ast} (K,N)\) metric measure spaces

This page was built for publication: Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds. II: Integral curvature condition