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, p. 1-22
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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.

DOI : https://doi.org/10.1016/j.anihpc.2013.09.005
Classification:  35B05,  35B65,  35J70
@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},
     publisher = {Elsevier},
     volume = {32},
     number = {1},
     year = {2015},
     pages = {1-22},
     doi = {10.1016/j.anihpc.2013.09.005},
     zbl = {1319.35051},
     mrnumber = {3303939},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPC_2015__32_1_1_0/

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