%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