naa a22 4500 510810942 CHVBK 20180411083442.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9310-8 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9310-8 Gradient Estimates for the Porous Medium Equations on Riemannian Manifolds [Elektronische Daten] [Guangyue Huang, Zhijie Huang, Haizhong Li] In this paper we study gradient estimates for the positive solutions of the porous medium equation: $$u_t=\Delta u^m$$ where m>1, which is a nonlinear version of the heat equation. We derive local gradient estimates of the Li-Yau type for positive solutions of porous medium equations on Riemannian manifolds with Ricci curvature bounded from below. As applications, several parabolic Harnack inequalities are obtained. In particular, our results improve the ones of Lu, Ni, Vázquez, and Villani (in J. Math. Pures Appl. 91:1-19, 2009). Moreover, our results recover the ones of Davies (in Cambridge Tracts Math vol. 92, 1989), Hamilton (in Comm. Anal. Geom. 1:113-125, 1993) and Li and Xu (in Adv. Math. 226:4456-4491, 2011). Mathematica Josephina, Inc., 2012 Porous medium equation nationallicence Li-Yau type estimate nationallicence Harnack inequality nationallicence Huang Guangyue Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut Huang Zhijie Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut Li Haizhong Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1851-1875 1050-6926 23:4<1851 2013 23 12220 https://doi.org/10.1007/s12220-012-9310-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9310-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang Guangyue Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut NATIONALLICENCE 700 1- Huang Zhijie Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut NATIONALLICENCE 700 1- Li Haizhong Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, P.R. China aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1851-1875 1050-6926 23:4<1851 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer