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