Liouville theorems and gradient estimates for a nonlinear elliptic equation

DOI10.1016/j.jde.2015.09.003zbMath1327.53047OpenAlexW1672693313WikidataQ125906763 ScholiaQ125906763MaRDI QIDQ888212

Lin-Feng Wang

Publication date: 4 November 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.09.003

zbMATH Keywords

gradient estimateHarnack inequalityLiouville theoremsmooth metric measure spaceBakry-Émery curvatureweighted Bochner formula

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (3)

Maximum principles involving the uniformly elliptic nonlocal operator ⋮ Positive solutions to semilinear elliptic equations involving a weighted fractional Lapalacian ⋮ Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds

Cites Work

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• Gradient estimates for the porous medium equations on Riemannian manifolds
• Aronson-Bénilan estimates for the porous medium equation under the Ricci flow
• Comparison geometry for the Bakry-Emery Ricci tensor
• The upper bound of the \({{\text L}_{\mu}^2}\) spectrum
• Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications

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