Aronson–Bénilan and Harnack estimates for the discrete porous medium equation

Aronson, 1979, Régularité des solutions de l’équation des milieux poreux dans Rn, C. R. Acad. Sci. Paris Sér. A-B, 288, 103 Auchmuty, 1994, Harnack-type inequalities for evolution equations, Proc. Amer. Math. Soc., 122, 117, 10.1090/S0002-9939-1994-1219716-X Bakry, 2017, The Li-Yau inequality and applications under a curvature-dimension condition, Ann. Inst. Fourier (Grenoble), 67, 397, 10.5802/aif.3086 Bakry, 2014, vol. 348 Bakry, 2006, A logarithmic Sobolev form of the Li-Yau parabolic inequality, Rev. Mat. Iberoam., 22, 683, 10.4171/RMI/470 Bauer, 2015, Li-Yau inequality on graphs, J. Differ. Geom., 99, 359, 10.4310/jdg/1424880980 Bianchi, 2022, The generalized porous medium equation on graphs: existence and uniqueness of solutions with ℓ1 data, Calc. Var. Partial Differential Equations, 61, 10.1007/s00526-022-02249-w Cao, 2015, Aronson-Bénilan estimates for the porous medium equation under the Ricci flow, J. Math. Pures Appl., 104, 729, 10.1016/j.matpur.2015.05.001 Dier, 2021, Discrete versions of the Li-Yau gradient estimate, Ann. Sc. Norm. Super. Pisa Cl. Sci., 22, 691 Erbar, 2014, Gradient flow structures for discrete porous medium equations, Discrete Contin. Dyn. Syst., 34, 1355, 10.3934/dcds.2014.34.1355 Kräss, 2022 Li, 2012 Li, 1986, On the parabolic kernel of the Schrödinger operator, Acta Math., 156, 153, 10.1007/BF02399203 Lu, 2009, Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds, J. Math. Pures Appl., 91, 1, 10.1016/j.matpur.2008.09.001 Münch, 2017, Remarks on curvature dimension conditions on graphs, Calc. Var. Partial Differential Equations, 56, 10.1007/s00526-016-1104-6 Münch, 2018, Li-Yau inequality on finite graphs via non-linear curvature dimension conditions, J. Math. Pures Appl., 120, 130, 10.1016/j.matpur.2018.10.006 Otto, 2001, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations, 26, 101, 10.1081/PDE-100002243 Spener, 2019, Curvature-dimension inequalities for non-local operators in the discrete setting, Calc. Var. Partial Differential Equations, 58, 10.1007/s00526-019-1616-y Vázquez, 2007 Weber, 2021, Entropy-information inequalities under curvature-dimension conditions for continuous-time Markov chains, Electron. J. Probab., 26, 10.1214/21-EJP627 Weber, 2021, The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains, J. Funct. Anal., 281, 10.1016/j.jfa.2021.109061