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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 873-877 (août 2010)
Doi : 10.1016/j.crma.2010.06.019
Received : 5 April 2010 ;  accepted : 17 June 2010
Liouville-type theorems for certain degenerate and singular parabolic equations
Théorèmes de type Liouville pour quelques équations paraboliques singulières dégénérées
 

Emmanuele DiBenedetto a , Ugo Gianazza b , Vincenzo Vespri c
a Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA 
b Dipartimento di Matematica “F. Casorati”, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy 
c Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy 

Abstract

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 ( ), and in the singular ( ) range.

The full text of this article is available in PDF format.
Résumé

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  , ainsi bien que dans le cas singulier  .

The full text of this article is available in PDF format.


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