Comptes Rendus
no. 15-16
Partial Differential Equations
Liouville-type theorems for certain degenerate and singular parabolic equations
[Théorèmes de type Liouville pour quelques équations paraboliques singulières dégénérées]

Présenté par : Pierre-Louis Lions

Emmanuele DiBenedetto1 ; Ugo Gianazza2 ; Vincenzo Vespri3
1 Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
2 Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy
Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 873-877.

En utilisant des résultats récents sur l'inégalité de Harnack pour les équations type p-laplacien, on établit des théorèmes de type Liouville pour les solutions de ces équations, dans le cas dégénéré p>2, ainsi bien que dans le cas singulier 1<p<2.

Relying on recent results on Harnack inequalities for equations of p-Laplacian type, we prove Liouville-type estimates for solutions to these equations, both in the degenerate (p>2), and in the singular (1<p<2) range.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.06.019
Emmanuele DiBenedetto 1 ; Ugo Gianazza 2 ; Vincenzo Vespri 3

1 Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
2 Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
3 Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy 
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     author = {Emmanuele DiBenedetto and Ugo Gianazza and Vincenzo Vespri},
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Emmanuele DiBenedetto; Ugo Gianazza; Vincenzo Vespri. Liouville-type theorems for certain degenerate and singular parabolic equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 873-877. doi : 10.1016/j.crma.2010.06.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.019/

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[3] E. DiBenedetto; U. Gianazza; V. Vespri Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Volume IX (2010), pp. 385-422

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