A sharp \(L^q\)-Liouville theorem for \(p\)-harmonic functions

DOI10.1007/BF02810597zbMath0955.31004OpenAlexW2040326204MaRDI QIDQ1972842

Ilkka Holopainen

Publication date: 28 February 2001

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02810597

zbMATH Keywords

Riemannian manifoldsubharmonic function

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (17)

Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Some nonlinear function theoretic properties of Riemannian manifolds ⋮ On the \(L ^{1}\)-Liouville property of stochastically incomplete manifolds ⋮ The pth Kazdan–Warner equation on graphs ⋮ The Liouville theorem for \(p\)-harmonic functions and quasiminimizers with finite energy ⋮ Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces ⋮ A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds ⋮ Euclidean volume growth for complete Riemannian manifolds ⋮ Liouville properties for 𝑝-harmonic maps with finite 𝑞-energy ⋮ \(p\)-capacity and \(p\)-hyperbolicity of submanifolds ⋮ Gradient estimate and Liouville theorems for \(p\)-harmonic maps ⋮ Analysis of weighted p-harmonic forms and applications ⋮ On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds ⋮ A sharp Liouville principle for \(\Delta_m u+u^p|\nabla u|^q\le 0\) on geodesically complete noncompact Riemannian manifolds ⋮ Some remarks on the weak maximum principle ⋮ Liouville type theorem for quasi-linear elliptic inequality \(\Delta_p u + u^\sigma \leqslant 0\) on Riemannian manifolds ⋮ On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds

Cites Work

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