%0 Journal Article %T Monotonicity in Half-Spaces of Positive Solutions to -Δpu = f (u) in the case p > 2 %+ Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA) %+ Università della Calabria [Arcavacata di Rende] (Unical) %A Farina, Alberto %A Montoro, Luigi %A Sciunzi, Berardino %< avec comité de lecture %@ 0391-173X %J Annali della Scuola Normale Superiore di Pisa, Classe di Scienze %I Scuola Normale Superiore %V 17 %N 4 %P 1207-1229 %8 2017 %D 2017 %Z Mathematics [math]Journal articles %X 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. %G English %2 https://u-picardie.hal.science/hal-03700891/document %2 https://u-picardie.hal.science/hal-03700891/file/Farina2017.pdf %L hal-03700891 %U https://u-picardie.hal.science/hal-03700891 %~ CNRS %~ UNIV-PICARDIE %~ INSMI %~ U-PICARDIE %~ LAMFA