Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. (English) Zbl 1156.58015
Summary: We derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman’s work we discover some new entropy formulae for these equations.
MSC:
| 58J90 | Applications of PDEs on manifolds |
| 35Q72 | Other PDE from mechanics (MSC2000) |
References:
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