Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition

Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition

We prove a global gradient estimate to positive solutions of the nonlinear parabolic equation ut=Δfu+auln⁡(u)+bu under an integral Bakry-Émery Ricci condition on compact weighted manifolds. The elliptic version of the equation arises in the study of gradient Ricci solitons and in this paper we consi...

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Veröffentlicht in:Differential geometry and its applications 2025-02, Vol.98, p.102222, Article 102222
Hauptverfasser: Olivé, Xavier Ramos, Seto, Shoo
Format: Artikel
Sprache:eng
Schlagworte:
Bakry-Émery-Ricci tensor
Gradient estimate
Integral Ricci curvature
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Zusammenfassung:We prove a global gradient estimate to positive solutions of the nonlinear parabolic equation ut=Δfu+auln⁡(u)+bu under an integral Bakry-Émery Ricci condition on compact weighted manifolds. The elliptic version of the equation arises in the study of gradient Ricci solitons and in this paper we consider the parabolic version.
ISSN:0926-2245
DOI:10.1016/j.difgeo.2024.102222