Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds

DOI10.1016/j.na.2011.05.008zbMath1223.35095OpenAlexW2092306901WikidataQ115343026 ScholiaQ115343026MaRDI QIDQ549951

Xiao Bao Zhu

Publication date: 19 July 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.05.008

zbMATH Keywords

local gradient estimate

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) A priori estimates in context of PDEs (35B45) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Positive solutions to PDEs (35B09) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

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Cites Work

• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• A matrix Harnack estimate for the heat equation
• Gradient estimate for the degenerate parabolic equation \(u_t=\Delta F(u)+H(u)\) on manifolds
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Differential equations on riemannian manifolds and their geometric applications

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