Gradient estimates via two-point functions for elliptic equations on manifolds

DOI10.1016/j.aim.2019.04.041zbMath1423.35114arXiv1808.09615OpenAlexW2949332115WikidataQ125315249 ScholiaQ125315249MaRDI QIDQ2417759

Ben Andrews, Changwei Xiong

Publication date: 29 May 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.09615

zbMATH Keywords

gradient estimatesquasilinear elliptic equations on Riemann manifolds

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Quasilinear elliptic equations (35J62) PDEs on manifolds (35R01)

Related Items (6)

Eigenvalue estimates on quaternion-Kähler manifolds ⋮ GRADIENT ESTIMATES VIA TWO-POINT FUNCTIONS FOR PARABOLIC EQUATIONS UNDER RICCI FLOW ⋮ Multi-point Maximum Principles and Eigenvalue Estimates ⋮ Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities ⋮ Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds ⋮ Sharp lower bound for the first eigenvalue of the weighted \(p\)-Laplacian. I

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stable solutions of elliptic equations on Riemannian manifolds
• Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
• Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations
• Liouville theorem for the nonlinear Poisson equation on manifolds
• Moduli of continuity for viscosity solutions on manifolds
• Comparison theorems in Finsler geometry and their applications
• Diffusion-type operators, Liouville theorems and gradient estimates on complete manifolds
• Finsler interpolation inequalities
• Regularity for a more general class of quasilinear equations
• An elementary method in the study of nonnegative curvature
• Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions.
• A pointwise gradient estimate for solutions of singular and degenerate PDE's in possibly unbounded domains with nonnegative mean curvature
• A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature
• A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature
• Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds
• Gradient bounds for anisotropic partial differential equations
• A sharp lower bound for the first eigenvalue on Finsler manifolds
• Linear and quasilinear elliptic equations
• Moduli of continuity for viscosity solutions
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Heat flow on Finsler manifolds
• Time-interior gradient estimates for quasilinear parabolic equations
• A gradient bound and a liouville theorem for nonlinear poisson equations
• User’s guide to viscosity solutions of second order partial differential equations
• A gradient bound for entire solutions of quasi‐linear equations and its consequences
• Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s

This page was built for publication: Gradient estimates via two-point functions for elliptic equations on manifolds