Gradient bounds and Liouville's type theorems for the Poisson equation on complete Riemannian manifolds

DOI10.2748/tmj/1178225458zbMath0847.58069OpenAlexW2008413657WikidataQ115227260 ScholiaQ115227260MaRDI QIDQ1908313

Marco Rigoli, Andrea Ratto

Publication date: 18 March 1996

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225458

zbMATH Keywords

Poisson equationGauss lemmagradient boundsLiouville type theoremscomplete Riemannian manifolds

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05)

Related Items (7)

Differential Harnack estimates for a nonlinear evolution equation of Allen-Cahn type ⋮ Some remarks on energy inequalities for harmonic maps with potential ⋮ Gradient estimates for the Allen-Cahn equation on Riemannian manifolds ⋮ Splitting theorems on complete Riemannian manifolds with nonnegative Ricci curvature ⋮ Diffusion-type operators, Liouville theorems and gradient estimates on complete manifolds ⋮ Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation ⋮ Gradient estimates for a class of semilinear parabolic equations and their applications

Cites Work

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• A gradient bound and a liouville theorem for nonlinear poisson equations
• Ground States for the Prescribed Mean Curvature Equation
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• Entire Solutions of Nonlinear Poisson Equations
• An Extension of Schwarz's Lemma

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