A uniform bound for the solutions to a simple nonlinear equation on Riemannian manifolds

DOI10.1016/j.na.2010.04.056zbMath1194.35172OpenAlexW2047408725WikidataQ115343046 ScholiaQ115343046MaRDI QIDQ988801

Bin Qian

Publication date: 19 August 2010

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.2010.04.056

zbMATH Keywords

curvaturenonlinear equationgradient estimates

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Semilinear elliptic equations (35J61)

Related Items (10)

Gradient estimates for a class of elliptic and parabolic equations on Riemannian manifolds ⋮ Gradient estimates and Liouville type theorems for a nonlinear elliptic equation ⋮ Gradient estimates for a simple nonlinear heat equation on manifolds ⋮ Gradient estimates for some semi-linear hypoelliptic equations ⋮ Harnack inequalities for simple heat equations on Riemannian manifolds ⋮ Gradient estimates and Liouville type theorems for \((p-1)^{p-1}\Delta_pu+au^{p-1}\log u^{p-1}=0\) on Riemannian manifolds ⋮ Yau type gradient estimates for \(\Delta u + au (\log u)^p + bu = 0\) on Riemannian manifolds ⋮ Remarks on differential Harnack inequalities ⋮ Gradient estimates for a nonlinear parabolic equation on complete smooth metric measure spaces ⋮ A new local gradient estimate for a nonlinear equation under integral curvature condition on manifolds

Cites Work

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• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Harnack inequality for non-self-adjoint evolution equations
• On the Harnack inequalities of partial differential equations
• Gradient estimate for the degenerate parabolic equation \(u_t=\Delta F(u)+H(u)\) on manifolds
• Harmonic functions on complete riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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