Gradient estimates for nonlinear elliptic equations involving the Witten Laplacian on smooth metric measure spaces and implications

DOI10.1515/anona-2022-0288OpenAlexW4322707505MaRDI QIDQ2688294

Yanyan Li

Publication date: 2 March 2023

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.01109

zbMATH Keywords

nonlinear elliptic equationsgradient estimatesWitten Laplaciansmooth metric measure spacesHarnack inequalitiesLiouville-type theoremsLi-Yau estimates

Mathematics Subject Classification ID

Diffusion processes (60J60) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Ricci flows (53E20)

Related Items

Souplet–Zhang and Hamilton‐type gradient estimates for non‐linear elliptic equations on smooth metric measure spaces ⋮ Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials ⋮ Hamilton and Li-Yau type gradient estimates for a weighted nonlinear parabolic equation under a super Perelman-Ricci flow

Cites Work

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• Gradient estimates for the equation \(\Delta u + cu ^{-\alpha} = 0\) on Riemannian manifolds
• Gradient estimates for the elliptic and parabolic Lichnerowicz equations on compact manifolds
• Yamabe-type equations on complete, noncompact manifolds
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Comparison geometry for the Bakry-Emery Ricci tensor
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• Gradient estimates for a class of parabolic systems
• A Yamabe-type problem on smooth metric measure spaces
• Li-Yau type estimates for a nonlinear parabolic equation on complete manifolds
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• A matrix Harnack estimate for the heat equation
• Positive solutions of Yamabe type equations on complete manifolds and applications
• Some geometric properties of the Bakry-Émery-Ricci tensor
• Gradient estimates for some \(f\)-heat equations driven by Lichnerowicz's equation on complete smooth metric measure spaces
• An infinite scale of incompressible twisting solutions to the nonlinear elliptic system \(\mathcal{L} [u; \mathsf{A}, \mathsf{B} = \nabla \mathcal{P}\) and the discriminant \(\varDelta(h, g)\)]
• Positive solutions to \(\Delta u-Vu+Wu^ p=0\) and its parabolic counterpart in noncompact manifolds.
• A Liouville-type theorem for smooth metric measure spaces
• On multiple solutions to a family of nonlinear elliptic systems in divergence form coupled with an incompressibility constraint
• Elliptic gradient estimates for a weighted heat equation and applications
• Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
• Gradient estimates for a nonlinear parabolic equation and Liouville theorems
• Hausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Recent Progress on Ricci Solitons
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• The Yamabe problem
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• On the elliptic equation Δ𝑢+𝑘𝑢-𝐾𝑢^{𝑝}=0 on complete Riemannian manifolds and their geometric applications
• The regularity of general parabolic systems with degenerate diffusion
• Function Spaces and Partial Differential Equations
• Elliptic-type gradient estimate for Schrödinger equations on noncompact manifolds
• Function Spaces and Partial Differential Equations
• Geometric Analysis
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials