A New proof of Liouville type theorems for a class of semilinear elliptic equations

2025/07/10 by Guo, Chen, Zhengce Zhang, Zhang, Zhengce · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2507.07664

Abstract

We study certain typical semilinear elliptic equations in Euclidean space \bRⁿ or on a closed manifold M with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method. Together with suitable integral estimates, some classical Liouville theorems will be reestablished.

Citations

• Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds
• Liouville type theorem for a class quasilinear p-Laplace type equation on the sphere
• Liouville-type theorems for the Lane-Emden equation in the half-space and cones
• Symmetry results for critical anisotropic p-Laplacian equations in\n convex cones
• Nonlinear flows and rigidity results on compact manifolds
• Local Gradient Estimate for p-harmonic functions on Riemannian Manifolds
• A Liouville-type Theorem for Smooth Metric Measure Spaces
• Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Global and local behavior of positive solutions of nonlinear elliptic equations

Cited by

• Classification of positive solutions to a class of Laplace equations with a gradient term

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