Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Monotonicity in half-spaces of positive solutions to -Delta(p)u = f(u) in the case p > 2

Abstract : We consider weak distributional solutions to the equation -Delta(p)u f(u) in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For p > 2 (the case 1 < p <= 2 is already known) we prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary of the half-space. As a consequence we deduce some Liouville-type theorems for the Lane-Emden-equation. Furthermore any nonnegative solution turns out to be C-2,C- (alpha) smooth.
Type de document :
Article dans une revue
Liste complète des métadonnées

https://hal-u-picardie.archives-ouvertes.fr/hal-03621419
Contributeur : Louise DESSAIVRE Connectez-vous pour contacter le contributeur
Soumis le : lundi 28 mars 2022 - 10:57:08
Dernière modification le : mercredi 14 septembre 2022 - 18:30:29

Identifiants

  • HAL Id : hal-03621419, version 1

Collections

Citation

Alberto Farina, Luigi Montoro, Berardino Sciunzi. Monotonicity in half-spaces of positive solutions to -Delta(p)u = f(u) in the case p > 2. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2017, 17 (4), pp.1207-1229. ⟨hal-03621419⟩

Partager

Métriques

Consultations de la notice

6