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.

@article{AIHPC_2015__32_1_1_0, author = {Farina, Alberto and Montoro, Luigi and Riey, Giuseppe and Sciunzi, Berardino}, title = {Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1--22}, publisher = {Elsevier}, volume = {32}, number = {1}, year = {2015}, doi = {10.1016/j.anihpc.2013.09.005}, mrnumber = {3303939}, zbl = {1319.35051}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.005/} }

TY - JOUR AU - Farina, Alberto AU - Montoro, Luigi AU - Riey, Giuseppe AU - Sciunzi, Berardino TI - Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 1 EP - 22 VL - 32 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.005/ DO - 10.1016/j.anihpc.2013.09.005 LA - en ID - AIHPC_2015__32_1_1_0 ER -

%0 Journal Article %A Farina, Alberto %A Montoro, Luigi %A Riey, Giuseppe %A Sciunzi, Berardino %T Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 1-22 %V 32 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.005/ %R 10.1016/j.anihpc.2013.09.005 %G en %F AIHPC_2015__32_1_1_0

Farina, Alberto; Montoro, Luigi; Riey, Giuseppe; Sciunzi, Berardino. Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 1-22. doi : 10.1016/j.anihpc.2013.09.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.09.005/

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