Yau type gradient estimates for \(\Delta u + au (\log u)^p + bu = 0\) on Riemannian manifolds

DOI10.1016/j.jmaa.2021.124963zbMath1461.53026arXiv2010.00776OpenAlexW3118438446WikidataQ115345886 ScholiaQ115345886MaRDI QIDQ1998639

Bo Peng, Guodong Wei, You-De Wang

Publication date: 7 March 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00776

zbMATH Keywords

gradient estimateRicci curvaturenonlinear elliptic equation

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Miscellaneous topics in partial differential equations (35R99)

Related Items (4)

Gradient estimates and Liouville theorems for Lichnerowicz equations ⋮ On the nonexistence of positive solution to \(\Delta u + au^{p+1} = 0\) on Riemannian manifolds ⋮ Gradient estimates for a class of elliptic and parabolic equations on Riemannian manifolds ⋮ Gradient estimate for solutions of the equation \(\Delta_p v +av^q=0\) on a complete Riemannian manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Elliptic gradient estimates for a nonlinear heat equation and applications
• Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational consequences
• Logarithmic Harnack inequalities
• Gradient estimates for positive smooth \(f\)-harmonic functions
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Gradient estimates for a weighted nonlinear elliptic equation and Liouville type theorems
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
• A uniform bound for the solutions to a simple nonlinear equation on Riemannian manifolds
• On the parabolic kernel of the Schrödinger operator
• Global heat kernel estimates
• Constrained and linear Harnack inequalities for parabolic equations
• Convergence from power-law to logarithm-law in nonlinear scalar field equations
• Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants
• Local behavior of solutions of some elliptic equations
• Harnack inequality for non-self-adjoint evolution equations
• Li-Yau estimates for a nonlinear parabolic equation on manifolds
• Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces
• Existence and concentration of positive solutions for a logarithmic Schrödinger equation via penalization method
• Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds
• Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
• Differential Harnack estimates for a nonlinear heat equation
• Differential Harnack estimates for time-dependent heat equations with potentials
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• Logarithmic Sobolev Inequalities
• Sharp gradient estimates for a heat equation in Riemannian manifolds
• A Harnack inequality for nonlinear equations
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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