A. , A user guide for the computation of the threshold time Let us recall what the threshold time is

D. G. Aronson and P. Bénilan, Régularité des solutions de l'équation des milieux poreux dans R N, C. R. Acad. Sci. Paris Sér. A-B, vol.288, pp.103-105, 1979.

D. G. Aronson and L. A. Caffarelli, The initial trace of a solution of the porous medium equation, Trans. Amer. Math. Soc, vol.280, pp.351-366, 1983.

D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Archive for Rational Mechanics and Analysis, vol.25, pp.81-122, 1967.

P. Bénilan and M. G. Crandall, Regularizing effects of homogeneous evolution equations, Contributions to analysis and geometry, pp.23-39, 1980.

A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo, and J. L. Vázquez, Asymptotics of the fast diffusion equation via entropy estimates, Archive for Rational Mechanics and Analysis, vol.191, pp.347-385, 2009.

E. Bombieri and E. Giusti, Harnack's inequality for elliptic differential equations on minimal surfaces, Inventiones Mathematicae, vol.15, pp.24-46, 1972.

, Harnack's inequality for elliptic differential equations on minimal surfaces, Inventiones Mathematicae, vol.15, pp.24-46, 1972.

M. Bonforte, J. Dolbeault, G. Grillo, and J. L. Vázquez, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Proceedings of the National Academy of Sciences of the United States of America, vol.107, pp.16459-16464, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00404718

M. Bonforte, J. Dolbeault, B. Nazaret, and N. Simonov, Stability in Gagliardo-Nirenberg inequalities
URL : https://hal.archives-ouvertes.fr/hal-02887010

M. Bonforte, G. Grillo, and J. L. Vázquez, Quantitative local bounds for subcritical semilinear elliptic equations, Milan Journal of Mathematics, vol.80, pp.65-118, 2012.

M. Bonforte and N. Simonov, Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights, 2020.

M. Bonforte and J. L. Vázquez, Global positivity estimates and Harnack inequalities for the fast diffusion equation, Journal of Functional Analysis, vol.240, pp.399-428, 2006.

, Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations, Advances in Mathematics, vol.223, pp.529-578, 2010.

P. Daskalopoulos and C. E. Kenig, Degenerate diffusions, Initial value problems and local regularity theory, EMS Tracts in Mathematics, vol.1, 2007.

M. , D. Pino, and J. Dolbeault, Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions, Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol.81, pp.847-875, 2002.

J. Denzler and R. J. Mccann, Phase transitions and symmetry breaking in singular diffusion, Proc. Natl. Acad. Sci. USA, vol.100, pp.6922-6925, 2003.

, Fast diffusion to self-similarity: complete spectrum, long-time asymptotics, and numerology, Archive for Rational Mechanics and Analysis, vol.175, pp.301-342, 2005.

E. Dibenedetto, Degenerate parabolic equations, 1993.

E. Dibenedetto, U. Gianazza, and V. Vespri, Harnack's inequality for degenerate and singular parabolic equations, Springer Monographs in Mathematics, 2012.

J. Dolbeault and G. Toscani, Fast diffusion equations: matching large time asymptotics by relative entropy methods, Kinetic and Related Models, vol.4, pp.701-716, 2011.

V. A. Galaktionov and J. L. Vázquez, A Stability Technique for Evolution Partial Differential Equations, 2004.

C. E. Gutiérrez and R. L. Wheeden, Mean value and Harnack inequalities for degenerate parabolic equations, Colloquium Mathematicum, vol.60, pp.157-194, 1990.

M. A. Herrero and M. Pierre, The Cauchy problem for u t = ?u m when 0 < m < 1, Transactions of the, vol.291, pp.145-158, 1985.

O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. , Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, 1995.

J. Moser, A Harnack inequality for parabolic differential equations, Communications on Pure and Applied Mathematics, vol.17, pp.101-134, 1964.

J. Moser, On a pointwise estimate for parabolic differential equations, Communications on Pure and Applied Mathematics, vol.24, pp.727-740, 1971.

G. Scheffer, Inégalités fonctionnelles, géométrie conforme et noyaux markoviens, vol.3, 2001.

N. Simonov, Fast diffusion equations with Caffarelli-Kohn-Nirenberg weights: regularity and asymptotics, 2020.

J. L. Vázquez, Smoothing and decay estimates for nonlinear diffusion equations, of Oxford Lecture Series in Mathematics and its Applications, vol.33, 2006.

, The porous medium equation, Mathematical theory, Oxford Mathematical Monographs, 2007.