×

Gradient estimates for positive smooth \(f\)-harmonic functions. (English) Zbl 1240.58019

Summary: For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth \(f\)-harmonic functions when the \(\infty\)-Bakry-Emery Ricci tensor and the Ricci tensor are bounded from below, and generalize the classical ones of Yau (i.e., when \(f\) is constant).

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K05 Heat equation
58C35 Integration on manifolds; measures on manifolds
PDFBibTeX XMLCite
Full Text: DOI