Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces
DOI10.1515/ANS-2023-0120MaRDI QIDQ6547806
Vahideh Vahidifar, Ali Karimi Taheri
Publication date: 31 May 2024
Published in: Advanced Nonlinear Studies (Search for Journal in Brave)
nonlinear parabolic equationsWitten Laplaciansmooth metric measure spacesLiouville type resultsLi-Yau estimatesdifferential Harnack inequalities
Nonlinear parabolic equations (35K55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- A splitting theorem for the weighted measure
- 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
- The upper bound of the \({{\text L}_{\mu}^2}\) spectrum
- Gradient estimates for the heat equation under the Ricci flow
- 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
- Some geometric properties of the Bakry-Émery-Ricci tensor
- On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
- Gradient estimates for some \(f\)-heat equations driven by Lichnerowicz's equation on complete smooth metric measure spaces
- Hamilton differential Harnack inequality and \(W\)-entropy for Witten Laplacian on Riemannian manifolds
- 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 \(\varDelta(h, g)\)
- Super-Ricci flows for metric measure spaces
- A Liouville-type theorem for smooth metric measure spaces
- Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds
- On multiple solutions to a family of nonlinear elliptic systems in divergence form coupled with an incompressibility constraint
- \(W\)-entropy, super Perelman Ricci flows, and \((K, m)\)-Ricci solitons
- Elliptic gradient estimates for a weighted heat equation and applications
- A Harnack inequality for the parabolic Allen-Cahn equation
- Differential Harnack estimates for Fisher's equation
- Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
- Gradient estimates for a nonlinear parabolic equation and Liouville theorems
- Differential Harnack inequalities and the Ricci flow
- Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
- The wave of advance of advantageous genes.
- Liouville theorems and elliptic gradient estimates for a nonlinear parabolic equation involving the Witten Laplacian
- 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
- Differential equations on riemannian manifolds and their geometric applications
- Logarithmic Sobolev Inequalities
- The regularity of general parabolic systems with degenerate diffusion
- Function Spaces and Partial Differential Equations
- Function Spaces and Partial Differential Equations
- Geometric analysis
- 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
- Gradient estimates for a weighted \(\Gamma\)-nonlinear parabolic equation coupled with a super Perelman-Ricci flow and implications
This page was built for publication: Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6547806)