Liouville theorem for the nonlinear Poisson equation on manifolds

DOI10.1016/j.jmaa.2014.03.005zbMath1311.53039OpenAlexW1972632706MaRDI QIDQ488766

Ingo Witt, Li Ma

Publication date: 26 January 2015

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.03.005

zbMATH Keywords

Liouville theoremnonlinear Poisson equationmodica-type gradient estimate

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (3)

Differential Harnack estimates for a nonlinear evolution equation of Allen-Cahn type ⋮ Some remarks on energy inequalities for harmonic maps with potential ⋮ Gradient estimates via two-point functions for elliptic equations on manifolds

Cites Work

• Unnamed Item
• Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergence
• Liouville type theorem and uniform bound for the Lichnerowicz equation and the Ginzburg-Landau equation
• A gradient bound and a liouville theorem for nonlinear poisson equations
• A gradient bound for entire solutions of quasi‐linear equations and its consequences

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