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Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds |
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| Authors: | Marc Arnaudon Anton Thalmaier Feng-Yu Wang |
| Affiliation: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;2. Département de mathématiques, Université de Poitiers, Téléport 2 - BP 30179, F–86962 Futuroscope Chasseneuil Cedex, France;3. Institute of Mathematics, University of Luxembourg, 162A, avenue de la Faïencerie, L–1511 Luxembourg, Luxembourg;4. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK |
| Abstract: | A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived. |
| Keywords: | 58J65 58J35 60H30 |
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