Monotonicity in Half-Spaces of Positive Solutions to -Δpu = f (u) in the Case p > 2 - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2017

Monotonicity in Half-Spaces of Positive Solutions to -Δpu = f (u) in the Case p > 2

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L. Montoro
  • Fonction : Auteur
B. Sciunzi
  • Fonction : Auteur

Résumé

We consider weak distributional solutions to the equation -Δpu = 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-type equation. Furthermore any nonnegative solution turns out to be C2'α smooth. \textcopyright 2017 Scuola Normale Superiore. All rights reserved.
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hal-03700891 , version 1 (21-06-2022)

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  • HAL Id : hal-03700891 , version 1

Citer

Alberto Farina, L. Montoro, B. Sciunzi. Monotonicity in Half-Spaces of Positive Solutions to -Δpu = f (u) in the Case p > 2. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2017, 17 (4), pp.1207--1229. ⟨hal-03700891⟩
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