Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds

DOI10.1090/proc/14106zbMath1398.58007arXiv1710.09519OpenAlexW2962987908WikidataQ115290780 ScholiaQ115290780MaRDI QIDQ4683545

Bingqing Ma, Yong Luo, Guangyue Huang

Publication date: 21 September 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.09519

zbMATH Keywords

nonlinear elliptic equationgradient estimatesLiouville-type theorem

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (8)

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 and Liouville type theorems for a weighted nonlinear \(p\)-Laplacian equation on compact smooth metric measure spaces ⋮ Gradient estimates for positive weak solution to \(\Delta_p u + au^\sigma = 0\) on Riemannian manifolds ⋮ Liouville type theorems for nonlinear \(p\)-Laplacian equation on complete noncompact Riemannian manifolds ⋮ GRADIENT ESTIMATES OF A NONLINEAR ELLIPTIC EQUATION FOR THE V -LAPLACIAN ⋮ Gradient estimates and Liouville type theorems for \((p-1)^{p-1}\Delta_pu+au^{p-1}\log u^{p-1}=0\) on Riemannian manifolds ⋮ Subgradient estimates for the equation \(\Delta_bu+cu^{-\alpha}=0\) on complete pseudohermitian manifolds

Cites Work

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• Yau's gradient estimates for a nonlinear elliptic equation
• Hamilton's gradient estimates of porous medium and fast diffusion equations
• Gradient estimates for the equation \(\Delta u + cu ^{-\alpha} = 0\) on Riemannian manifolds
• Gradient estimates and Liouville type theorems for a nonlinear elliptic equation
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• Liouville type theorems of a nonlinear elliptic equation for the \(V\)-Laplacian
• A Liouville-type theorem for smooth metric measure spaces
• Hausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Harmonic functions on complete riemannian manifolds

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