Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

DOI10.1007/s10114-011-8474-7zbMath1219.58012OpenAlexW2113900213WikidataQ115385251 ScholiaQ115385251MaRDI QIDQ546355

Bin Qian

Publication date: 24 June 2011

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-011-8474-7

zbMATH Keywords

nonlinear parabolic equationsgradient estimatesHarnack differential inequalitiesLi-Yau inequalities

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

Differential Harnack inequality for a parabolic equation under the Finsler-geometric flow ⋮ Harnack estimates for a nonlinear parabolic equation under Ricci flow ⋮ Gradient estimates for a nonlinear diffusion equation on complete manifolds ⋮ Revisiting Li-Yau type inequalities on Riemannian manifolds ⋮ The \(\alpha\)-geometric structures on manifold of positive definite Hermite matrices ⋮ Gradient estimates for a parabolic 𝑝-Laplace equation with logarithmic nonlinearity on Riemannian manifolds ⋮ Li-Yau estimates for a nonlinear parabolic equation on manifolds ⋮ Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces ⋮ Gradient estimates for a nonlinear parabolic equation on complete smooth metric measure spaces

Cites Work

• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• Gradient estimate for Schrödinger operators on manifolds
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• Gradient estimates and a Liouville type theorem for the Schrödinger operator
• Gradient estimate for the degenerate parabolic equation \(u_t=\Delta F(u)+H(u)\) on manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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