Li-Yau inequality for heat equations on \(RCD^\ast (K, N)\) metric measure spaces

DOI10.1007/s11118-019-09770-2zbMath1448.58021OpenAlexW2912531976MaRDI QIDQ778184

Jia-Cheng Huang

Publication date: 2 July 2020

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-019-09770-2

zbMATH Keywords

heat equationLi-Yau inequality

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Weak solutions to PDEs (35D30) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) PDEs on manifolds (35R01)

Related Items (1)

Differential Harnack inequalities for semilinear parabolic equations on \(\mathrm{RCD}^{\ast} (K,N)\) metric measure spaces

Cites Work

• Unnamed Item
• On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces
• Sharp spectral gaps on metric measure spaces
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Local Li-Yau's estimates on \(RCD^\ast(K,N)\) metric measure spaces
• Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
• Ricci curvature on Alexandrov spaces and rigidity theorems
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• Weak curvature conditions and functional inequalities
• Hamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spaces
• Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• The Li-Yau inequality and applications under a curvature-dimension condition
• Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces
• Remarks on differential Harnack inequalities
• Li-Yau inequality on graphs
• The Li-Yau inequality and heat kernels on metric measure spaces
• Ricci curvature for metric-measure spaces via optimal transport
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• On the geometry of metric measure spaces. I
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Li-Yau and Harnack type inequalities in \(\text{RCD}^\ast (K,N)\) metric measure spaces
• Alexandrov meets Lott--Villani--Sturm
• Li-Yau gradient bound for collapsing manifolds under integral curvature condition
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Neumann Li-Yau gradient estimate under integral Ricci curvature bounds
• Generalized Li−Yau estimates and Huisken’s monotonicity formula

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