Hardy-Poincaré inequalities and applications to nonlinear diffusions

Comptes Rendus Mathematique

Volumn 344, Issue 7, 2007, Pages 431-436

  Blanchet, Adrien ^a   Bonforte, Matteo ^a   Dolbeault, Jean ^a   Grillo, Gabriele ^b   Vázquez, Juan Luis ^c  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b POLITECNICO DI TORINO   (Italy)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947729430     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.01.011     Document Type: Article

References (15)

1. A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo, J.L. Vázquez, Asymptotics of the fast diffusion equation, in preparation
2. Bonforte M., and Vázquez J.L. Global positivity estimates and Harnack inequalities for the fast diffusion equation. J. Funct. Anal. 240 (2006) 399-428
3. Carrillo J.A., Lederman C., Markowich P.A., and Toscani G. Poincaré inequalities for linearizations of very fast diffusion equations. Nonlinearity 15 (2002) 565-580
4. Carrillo J.A., and Vázquez J.L. Fine asymptotics for fast diffusion equations. Comm. Partial Differential Equations 28 (2003) 1023-1056
5. Cipriani F. Sobolev-Orlicz imbeddings, weak compactness, and spectrum. J. Funct. Anal. 177 (2000) 89-106
6. P. Daskalopoulos, N. Sesum, On the extinction profile of solutions to fast-diffusion, 2006
7. Davies E.B. A review of Hardy inequalities. The Maz'ya Anniversary Collection, vol. 2. Rostock, 1998. Oper. Theory Adv. Appl. vol. 110 (1999), Birkhäuser, Basel 55-67
8. p (Ω). Math. Z. 227 (1998) 511-523
9. Del Pino M., and Dolbeault J. Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. J. Math. Pures Appl. (9) 81 (2002) 847-875
10. Denzler J., and McCann R.J. Fast diffusion to self-similarity: complete spectrum, long-time asymptotics, and numerology. Arch. Ration. Mech. Anal. 175 (2005) 301-342
11. Grillo G. On Persson's theorem in local Dirichlet spaces. Z. Anal. Anwend. 17 (1998) 329-338
12. Muckenhoupt B. Hardy's inequality with weights. Studia Math. 44 (1972) 31-38 Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, I
13. Persson A. Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator. Math. Scand. 8 (1960) 143-153
14. Piepenbrink J. Integral inequalities and theorems of Liouville type. J. Math. Anal. Appl. 26 (1969) 630-639
15. Vázquez J.L. Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Oxford Lecture Ser. Math. Appl. vol. 33 (2006), Oxford Univ. Press