Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces

Farina, Alberto; Montoro, Luigi; Riey, Giuseppe; Sciunzi, Berardino

Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 1-22.

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.

Classification: 35B05, 35B65, 35J70

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