Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces
Alberto Farina, Luigi Montoro, Giuseppe Riey, Berardino Sciunzi · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2013
We consider a quasilinear elliptic equation involving a first-order term, under zero Dirichlet boundary condition in half-spaces. We prove that any positive solution is monotone increasing with respect to the direction orthogonal to the boundary. The main ingredient in the proof is a new comparison principle in unbounded domains. As a consequence of our analysis, we also obtain some new Liouville type theorems.