Behaviour near extinction for the Fast Diffusion Equation on bounded domains

Adimurthi, 1994, An elementary proof of the uniqueness of positive radial solutions of a quasilinear Dirichlet problem, Arch. Rational Mech. Anal., 127, 219, 10.1007/BF00381159

Aronson, 1981, Large time behaviour of solutions of the porous medium equation in bounded domains, J. Diff. Eq., 39, 378, 10.1016/0022-0396(81)90065-6

Ashbaugh, 1988, Optimal lower bounds for eigenvalues gaps for Schrödinger operators with symmetric single-well potentials and related results, vol. 175

Berryman, 1980, Stability of the separable solution for fast diffusion, Arch. Rational Mech. Anal., 74, 379, 10.1007/BF00249681

Blanchet, 2007, Hardy–Poincaré inequalities and applications to nonlinear diffusions, C. R. Math. Acad. Sci. Paris, 344, 431, 10.1016/j.crma.2007.01.011

Blanchet, 2009, Asymptotics of the fast diffusion equation via entropy estimates, Arch. Rational Mech. Anal., 191, 347, 10.1007/s00205-008-0155-z

Bonforte, 2010, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Proc. Natl. Acad. Sci. USA, 107, 16459, 10.1073/pnas.1003972107

Bonforte, 2010, Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold, Arch. Rational Mech. Anal., 196, 631, 10.1007/s00205-009-0252-7

M. Bonforte, G. Grillo, J.L. Vázquez, Quantitative bounds for semilinear elliptic equations, preprint.

Bonforte, 2006, Global positivity estimates and Harnack inequalities for the fast diffusion equation, J. Funct. Anal., 240, 399, 10.1016/j.jfa.2006.07.009

Bonforte, 2010, Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations, Advances in Math., 223, 529, 10.1016/j.aim.2009.08.021

Brezis, 1977, On a class of superlinear elliptic problems, Comm. PDE, 2, 601, 10.1080/03605307708820041

Budd, 1987, Semilinear elliptic equations and supercritical growth, J. Diff. Eq., 68, 169, 10.1016/0022-0396(87)90190-2

Chen, 1988, On the local behaviour of solutions of singular parabolic equation, Arch. Rational Mech. Anal., 103, 319, 10.1007/BF00251444

Davies, 1989

de Figueiredo, 1982, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl., 61, 41

del Pino, 2001, On the extinction profile for solutions of ut=Δu(N+2)/(N−2), Indiana Univ. Math. J., 50, 611, 10.1512/iumj.2001.50.1876

del Pino, 2007, Boundary singularities for weak solutions of semilinear elliptic problems, J. Funct. Anal., 253, 241, 10.1016/j.jfa.2007.05.023

DiBenedetto, 1993

DiBenedetto, 2010, Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., IX, 385

DiBenedetto, 1992, Harnack estimates and extinction profile for weak solution of certain singular parabolic equations, Trans. Amer. Math. Soc., 330, 783, 10.1090/S0002-9947-1992-1076615-7

DiBenedetto, 1991, Local space-analyticity of solutions of certain singular parabolic equations, Indiana Univ. Math. J., 40, 741, 10.1512/iumj.1991.40.40033

Feireisl, 2000, Convergence for semilinear degenerate parabolic equations in several space dimension, J. Dyn. Diff. Eq., 12, 647, 10.1023/A:1026467729263

Gagliardo, 1958, Proprietà di alcune classi di funzioni in piú variabili, Ricerche Mat., 7, 102

Galaktionov, 2004, A Stability Technique for Evolution Partial Differential Equations, a Dynamical System Approach, vol. 56

Gidas, 1979, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68, 209, 10.1007/BF01221125

Gilbarg, 1977, Elliptic Partial Differential Equations of Second Order, vol. 224

Ladyzhenskaya, 1968, Linear and Quasilinear Equations of Parabolic Type, vol. 23

Ling, 1993, A lower bound for the gap between the first two eigenvalues of Schrödinger operators on convex domains in Sn or Rn, Michigan Math. J., 40, 259, 10.1307/mmj/1029004752

Ni, 1985, Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0, Comm. Pure Appl. Math., 38, 67, 10.1002/cpa.3160380105

Nirenberg, 1959, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13, 115

Pucci, 2007, The Maximum Principle, vol. 73

Singer, 1985, An estimate of the gap of the first two eigenvalues in the Schrödinger operator, Ann. Scuola Norm. Sup. Pisa, XII, 319

Smits, 1996, Spectral gaps and rates to equilibrium for diffusions in convex domains, Michigan Math. J., 43, 141, 10.1307/mmj/1029005394

Vázquez, 2003, Asymptotic behaviour for the Porous Medium Equation posed in the whole space, J. Evol. Eq., 3, 67, 10.1007/s000280300004

Vázquez, 2004, The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behaviour, Monatsh. Math., 142, 81, 10.1007/s00605-004-0237-4

Vázquez, 2006, Smoothing and Decay Estimates for Nonlinear Diffusion Equations, vol. 33

Vázquez, 2007, The Porous Medium Equation. Mathematical Theory

Yu, 1986, Lower bounds of the gap between the first and second eigenvalues of the Schrödinger operator, Trans. Amer. Math. Soc., 294, 341