Gradient estimates for a weighted nonlinear elliptic equation and Liouville type theorems

DOI10.1016/j.geomphys.2020.103737zbMath1442.35489OpenAlexW3026923731MaRDI QIDQ778979

Abimbola Abolarinwa

Publication date: 21 July 2020

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2020.103737

zbMATH Keywords

Riemannian manifoldsLiouville theoremelliptic equationsYamabe problemgradient estimates

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) PDEs on manifolds (35R01)

Related Items (7)

Gradient estimates of positive solutions for the weighted nonlinear parabolic equation ⋮ Gradient estimations for nonlinear elliptic equations on weighted Riemannian manifolds ⋮ Gradient estimates and Liouville type theorems for a weighted nonlinear \(p\)-Laplacian equation on compact smooth metric measure spaces ⋮ Yau type gradient estimates for \(\Delta u + au (\log u)^p + bu = 0\) on Riemannian manifolds ⋮ Gradient estimates for a nonlinear parabolic equation on complete smooth metric measure spaces ⋮ Gradient and Hessian estimates for an elliptic equation on smooth metric measure spaces ⋮ Triviality of bounded solutions and gradient estimates for nonlinear \(f\)-heat equations on complete smooth metric measure spaces

Cites Work

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• A Liouville-type theorem for smooth metric measure spaces
• Li-Yau estimates for a nonlinear parabolic equation on manifolds
• Logarithmic-Sobolev and multilinear Hölder's inequalities via heat flow monotonicity formulas
• Gradient estimates for a nonlinear elliptic equation on complete noncompact Riemannian manifold

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